avg q8

[Saumyojit]

Read the passage and I am stuck in question 40

For 15 overs both Das and Dasgupta scored = ( 4 * 15 + 2 * 15 ) = 90 runs

Dasgupta changed his gears to normal after 20 overs

For the next 5 overs both scored = ( 5 * 5 + 2 * 5 ) = 35 runs

For the next 2 overs = ( 5 * 2 + 3* 2 ) = 16 runs


Expected score after 22 overs = 141 runs

 

[BigBeachBanana]

I think this is a poorly written question, but you need to divide your answer by two as the question asks for the expected score of the partnership, i.e., the weighted average of both players. What you've calculated is the expected score for both players. Each player batted 22 overs, hence divided by 2.

Alternative solution:
E[runs |Das] = 15*4 + 5*7 = 95
E[runs |Dasgupta] = 20*2 +2*3 = 46
E[runs]=E[E|batter]] = E[runs |Das]*Pr(Das) + E[runs |Dasgupta]*Pr(Dasgupta) = 95*(22/44) + 46*(22/44) = 70.5

 

[Saumyojit]

I think this is a poorly written question, but you need to divide your answer by two as the question asks for the expected score of the partnership, i.e., the weighted average of both players. What you've calculated is the expected score for both players. Each player batted 22 overs, hence divided by 2.

Alternative solution:
E[runs |Das] = 15*4 + 5*7 = 95
E[runs |Dasgupta] = 20*2 +2*3 = 46
E[runs]=E[E|batter]] = E[runs |Das]*Pr(Das) + E[runs |Dasgupta]*Pr(Dasgupta) = 95*(22/44) + 46*(22/44) = 70.5

Expected score after 22 overs means to me sum of the runs scored by one batsmen in x balls and another batsmen in y balls where x+y will add up to 132 balls as each over means 6 balls.

What I had done is wrong as I have considered each batting for 22 overs.

Dasgupta changed his gears to normal after 20 overs

For the next 5 overs both scored = ( 5 * 5 + 2 * 5 ) = 35 runs

For the next 2 overs = ( 5 * 2 + 3* 2 ) = 16 runs


Expected score after 22 overs = 141 runs

This is wrong!

Each player batted 22 overs, hence divided by 2.

No.

But the question answer is 71 or 70.5 rounded off

 

[BigBeachBanana]

Expected score after 22 overs means to me sum of the runs scored by one batsmen in x balls and another batsmen in y balls where x+y will add up to 132 balls as each over means 6 balls.

What I had done is wrong as I have considered each batting for 22 overs.




This is wrong!



No.

But the question answer is 71 or 70.5 rounded off

Are you saying my answer is wrong or are you questioning your reasoning? The Direction for questions 40-41 instructs you to round your runs to the next whole number

 

[Saumyojit]

Are you saying my answer is wrong

the answer matches but the logic " Each player batted 22 overs " is wrong as both of batted together for 22 overs .

And if it is each for 22 , then that means the question is poorly worded . ABsolute baffling question again!!!!

 

[BigBeachBanana]

the answer matches but the logic " Each player batted 22 overs " is wrong as both of batted together for 22 overs .

And if it is each then that means the question is poorly worded . ABsolute baffling question again

They can't possibly be batted together 22 overs, must be 22 overs for each batter i.e the total is 44 overs. Because they question told you "Das batted.... 15 overs then turn,..., Dasgupta started off 20 overs then turns...". This doesn't make sense if they batted together 22 overs. It must be that each batter batted 22 overs in the partnership. The question is worded poorly. Maybe it meant to test your deductive reasoning. Who knows?

 

[Deleted member 4993]

They can't possibly be batted together 22 overs, must be 22 overs for each batter i.e the total is 44 overs. Because they question told you "Das batted.... 15 overs then turn,..., Dasgupta started off 20 overs then turns...". This doesn't make sense if they batted together 22 overs. It must be that each batter batted 22 overs in the partnership. The question is worded poorly. Maybe it meant to test your deductive reasoning. Who knows?

BBB, without getting into long explanation,

They can't possibly be batted together 22 overs

in cricket, there are 10 outs / inning. It is possible to express "batted together". There is always two batsman on the "pitch".

 

[Saumyojit]

it meant to test your deductive reasoning. Who knows?

yeah should have thought deeply! .
The question now makes Sense .

But , question was asked about estimated score after 22 overs so it will be 141 runs .
If they are asking for 71 runs then acc to me The question should be rephrased to " run rate of each batsman in partnership " then i would have done :
Avg run rate per batsman = Sum of the runs of 2 batsman / No of batsman

=> 141 / 2 = 70.5


Isn't it ?



They have said in the question
run rate of a partnership = Wt avg of run rates of two batsman involved weighted by ratio of no of balls faced by each batsman .

What does it mean in this case?

 

[BigBeachBanana]

But , question was asked about estimated score after 22 overs so it will be 141 runs

141 is the expected score of 44 overs (22 from Das and 22 from Dasgupta), not 22. The question asks the expected score after 22 overs, so you take the average of both batters. Since each contributed evenly, 22/44=>1/2; then the weighted average becomes a simple average=> 141/2.

The question should be rephrased to " run rate of each batsman in partnership " then i would have done :
Avg run rate per batsman = Sum of the runs of 2 batsman / No of batsman

If the question asked: "What's the run rate of each batmans in the partnership?" then you would need two answers. The answer would've been
E[runs |Das] = 15*4 + 5*7 = 95
E[runs |Dasgupta] = 20*2 +2*3 = 46

They have said in the question
run rate of a partnership = Wt avg of run rates of two batsman involved weighted by ratio of no of balls faced by each batsman .

What does it mean in this case?

I am unfamiliar with cricket, so I don't know what "the number of balls faced by each batsman" means. Maybe @Subhotosh Khan can explain. But the general idea of weighted average is to assign heavier weights to the player who contributes more, and vice versa.
$$Wt(Das)=\frac{\text{number of ball Das faced}}{\text{total balls both faced}}$$Similarly,
$$Wt(Dasgupta)=\frac{\text{number of ball Dasgupta faced}}{\text{total balls both faced}}$$As you can see, if Das faced more balls than Dasgupta, whatever that means, Das would have greater weight as he contributed more to the partnership.
The sum of weights must always equal 1, and a simple average is a particular case of weighted average where all the weights are equal.
$$Wt(Das) + Wt(Dasgupta) =1$$

 

[Saumyojit]

141 is the expected score of 44 overs (22 from Das and 22 from Dasgupta), not 22

yeah .
When talked about expected score after 22 overs it means avg runs scored by each batsman in the partnership is 71.5 runs .
Yeah now i understood .

"What's the run rate of each batmans in the partnership?

ok . We needed to find out each individual scores .

"the number of balls faced by each batsman"

132 balls each .

I think this is a poorly written question

Now after all the reasoning I think the question is alright.
What makes you think the question is poorly written ?

 

[Saumyojit]

Question 42
Tendulkar will come to bat after the first & second partnership is broken .

So , in the first partnership in 44 overs 141 runs were scored , then some runs 'x' will be scored in second partnership .

Out of 360 runs when tendulkar walks out the target remains is (360 - (140+x) ) to complete in ( 90 - ( 44+y )) Overs.


Just check am I saying something Wrong or not

avg runs scored by each batsman in 22 overs in the First partnership is 71runs .

And run rate per over of the first partnership is = Sum of the runs of both the batsman in 44 Overs divided by total balls

44 overs means 264 balls .

144 / 264 = 0.534 runs per ball

Then per over it will be 0.534 * 6 = 3.204= 3 runs per over

Is this right?





Assume Das is out , then second partnership is between dasgupta and dravid then their run rate is 2.5 per over .(as Specified in the question)

Now in the question it is said that he shares strikes equally and gets maximum support .

What does it tell or how does it give a hint in solving the problem

 

[Saumyojit]

@Dr.Peterson @BigBeachBananas

 

[BigBeachBanana]

And run rate per over of the first partnership is = Sum of the runs of both the batsman in 44 Overs divided by total balls

44 overs means 264 balls .

144 / 264 = 0.534 runs per ball

Then per over it will be 0.534 * 6 = 3.204= 3 runs per over

Is this right?

You can do 141 runs /44 overs = 3.2

Assume Das is out , then second partnership is between dasgupta and dravid then their run rate is 2.5 per over .(as Specified in the question)

Now in the question it is said that he shares strikes equally and gets maximum support .

What does it tell or how does it give a hint in solving the problem

I'm unfamiliar with cricket, so I'm not sure I can help. But

1. How do you know that Das is out, but not Dasgupta? Where in the question say that? Maybe this doesn't matter.
2. Let's say Das is out. How do you know Dravid is the next partnership? Is this going in order of the table?
3. 2.5/over when he walked out could be the average of all the batters went before, not necessarily the last partnership. How many partnerships have been until Tendulkar's?
4. What does a strike mean?
5. Who's Tendulkar partner?
6. The keyword in the parenthesis is "equally", possibly hinting to say equal weights.

 

[Saumyojit]

How do you know that Das is out, but not Dasgupta? Where in the question say that? Maybe this doesn't matter.

just assuming.

Let's say Das is out. How do you know Dravid is the next partnership? Is this going in order of the table?

yes.

2.5/over when he walked out could be the average of all the batters went before, not necessarily the last partnership. How many partnerships have been until Tendulkar's?

There have been two partnerships before Tendulkar came out .
2.5/over when he walked out could be the average of all the batters went before . Yes i agree

some runs 'x' will be scored in second partnership .

2.5 = ( 6 * (Sum of the runs scored by first three batsman ) ) / Total no of balls

2.5 = ( 6 * ( 141 + x ) ) / ( 44 *6 + 6y ) = _______

What does a strike mean?

when a batsman faces a ball from a bowler .

Who's Tendulkar partner?

anyone of dravid , das , dasgupta .

The keyword in the parenthesis is "equally", possibly hinting to say equal weights.

hmm. how?

 

[BigBeachBanana]

I'm guessing the number of overs in each partnership changes (again, I'm unfamiliar with cricket), so it's not 22 overs?
There has been a total of 2 partnerships before Tendulkar's turn.
Partnership #1: Das and Dasgupta
Partnership #2: Das/Dasgupta with Dravid
You know the run rate for partnership#1, and also you are given the aggregate average run rate (2.5run/over). Can you solve for how many runs partnership#2 scored?
Also, there's no reason to bring 'balls' into your formula. It says 2.5 runs/over, not runs/ball.
$$\frac{141 + x}{44 + y} =2.5 \frac{\text{runs}}{\text{over}}$$Lastly, the target run rate might be useful (360runs/90overs)

 

[Saumyojit]

You know the run rate for partnership#1, and also you are given the aggregate average run rate (2.5). Can you solve for how many runs partnership#2 two scored?

yeah i should have seen it .
after 88.28 overs tendulkar walks in

First partnership avg run rate per over = 3.2 runs

Aggregate average run rate of first two partnership 2.5= ( 3.2 + z ) / 2

z =1.8 (Avg Run rate per over of 2nd partnership )

1.8 = Total no of runs scored by two batsman / Total no of overs taken

1.8 = x / y


Now there is another equation 2.5 = Total no of runs scored by first three batsman / Total no of overs
Total no of overs = 44 + y

2.5 = (141 + x ) / (44 +y)

y =44.28 overs

The second partnership will play for 44.28 overs that means after 88.28 overs tendulkar walks in

 

[BigBeachBanana]

yeah i should have seen it .
after 88.28 overs tendulkar walks in

First partnership avg run rate per over = 3.2 runs

Aggregate average run rate of first two partnership 2.5= ( 3.2 + z ) / 2

z =1.8 (Avg Run rate per over of 2nd partnership )

1.8 = Total no of runs scored by two batsman / Total no of overs taken

1.8 = x / y


Now there is another equation 2.5 = Total no of runs scored by first three batsman / Total no of overs
Total no of overs = 44 + y

2.5 = (141 + x ) / (44 +y)

y =44.28 overs

The second partnership will play for 44.28 overs that means after 88.28 overs tendulkar walks in

You found how many runs there had been before Tendulkar walked in, which still didn't answer the question. Again, they need 360/90 to win. When is it too late? Consider the best/worst-case scenarios.
Regardless, it's already passed 60 overs which makes me think about whether the partnership lined up in the table's order, as you said.

Is this a possible scenario?
Say after partnership#1, both out. Then partnership#2 is Dravid and Telkundar. The 2.5 run rate is of the 3 batters Das, Dasgupta & Dravid.

 

[Saumyojit]

You found how many runs there had been before Tendulkar walked in, which still didn't answer the question

before tendulkar comes runs scored is 154.2 in 88.28 overs .

So , there is no way tendulkar along with other in 3rd partnership can win the match as runs left ( 360 - 154.2) in 1 over 4 balls .

Say after partnership#1, both out

when a partnership is broken then anyone gets out not both.

Consider the best/worst-case scenarios.

yeah i should have seen it .
after 88.28 overs tendulkar walks in

First partnership avg run rate per over = 3.2 runs

Aggregate average run rate of first two partnership 2.5= ( 3.2 + z ) / 2

z =1.8 (Avg Run rate per over of 2nd partnership )

1.8 = Total no of runs scored by two batsman / Total no of overs taken

1.8 = x / y


Now there is another equation 2.5 = Total no of runs scored by first three batsman / Total no of overs
Total no of overs = 44 + y

2.5 = (141 + x ) / (44 +y)

y =44.28 overs

The second partnership will play for 44.28 overs that means after 88.28 overs tendulkar walks in

acc to given data in question (Aggregate average run rate of first two partnerships= 2.5) we deduced that y =44.28 overs

partnership#2 is Dravid and Telkundar.

never.

 

[BigBeachBanana]

The issue with your calculation (3.2 +x)/2 = 2.5 is that you're assuming equal weights between the partnerships, i.e. you're saying the # of overs in partnership#1 = partnership#2. Without any further calculation and based on this assumption, we already know it will be 88 overs (44x2). I don't think it sensible for them to write a question like this where Teldunar walks out when it's already impossible to win. The answer choices suggest otherwise.
Recap what we know so far,
$$\frac{141 + x}{44 + y} =2.5 \frac{\text{runs}}{\text{over}}$$Our target is 360/90=> 4 runs/over
Telkundar need to score (360-141-x) runs to within (90-44-y) overs
Can you set up an inequality assuming the best-case scenario where he bats aggressively while scoring the most runs, he still loses, simply because there are enough overs for him to bat?

 

[Saumyojit]

The issue with your calculation (3.2 +x)/2 = 2.5 is that you're assuming equal weights

Yes

In second partnership Avg run rate per over (Avg) = x runs scored by Dravid along with his partner / y overs

Avg Run rate per over of two partnerships
2.5 = (Avg run rate per over of first partnership + Avg run rate per over of second partnership ) / 2 =

Tendulkar along with his partner has to score ( 360 - ( 141 + x ) ) runs within ( 90 - 44 - y) overs .

Tendulkar scores 8 runs per over when he bats aggressively .

Can you set up an inequality assuming the best-case scenario where he bats aggressively while scoring the most runs, he still loses, simply because there are enough overs for him to bat?

Suppose the 2nd partnership broke on the first ball only , then sachin has 45 overs 5 balls to score 219 runs along with his partner . Then he needs 27 overs playing aggressively to reach 219 runs but he shares the strike with other batsman too so it means either the batsman will not score so Sachin will play alone or both will contribute .




having a hard time to set it up.