Biased Dice Question: biased so that i lands on 1 one quarter of the time.

Loren Gray

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a dice is biased so that i lands on 1 one quarter of the time. it lands on 3 twice as often as it land on 2 and three times as often as it lands on 4. it lands on 5 ten percent more often than it lands on 4 and ten percent less often than it lands on 6. if i roll the dice 350 times, how often should i expect to roll a 6?

Please show how you worked it out! Thanks :)
 
a dice is biased so that it lands on 1 one quarter of the time. it lands on 3 twice as often as it land on 2 and three times as often as it lands on 4. it lands on 5 ten percent more often than it lands on 4 and ten percent less often than it lands on 6. if i roll the dice 350 times, how often should i expect to roll a 6?

Please show how you worked it out! Thanks :)
"Dice" is two.
"Die" is one.

p(1) = ___
P(2) = ___
p(3) = ___
p(4) = ___
p(5) = ___
p(6) = ___

That's a good start. Now, fill in the blanks - one hint at a time.

it lands on 1 one quarter of the time.

p(1) = 0.25
P(2) = ___
p(3) = ___
p(4) = ___
p(5) = ___
p(6) = ___

it lands on 3 twice as often as it land on 2

p(1) = 0.25
P(2) = ___
p(3) = 2 * p(2)
p(4) = ___
p(5) = ___
p(6) = ___

Continue...
 
No, excuse me, but you need to show us how you worked it out. And if you can't, then please tell us where you are stuck and we will guide you through the next step. We are here to help you figure out how to do the problem, not do it for you.
 
Three times as often as it lands on 4.

p(1) = 0.25

P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = ___
p(6) = ___

Lands on 5 10% more than it lands on 4.
0.3+10%=0.33
p(1) = 0.25
P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = (6*p(2))+10%
p(6) = ___

10% less often than it lands on 6.
p(1) = 0.25
P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = (6*p(2))+10%
p(6) = (6*p(2))-10%

not sure if this is right or about what to do next.
 
Three times as often as it lands on 4.

p(1) = 0.25

P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = ___
p(6) = ___

Lands on 5 10% more than it lands on 4.
0.3+10%=0.33
p(1) = 0.25
P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = (6*p(2))+10%
p(6) = ___

10% less often than it lands on 6.
p(1) = 0.25
P(2) = p(3)/2
p(3) = 2 * p(2)
p(4) = 6 * p(2)
p(5) = (6*p(2))+10%
p(6) = (6*p(2))-10%

not sure if this is right or about what to do next.

three times as often as it lands on 4.

p(1) = 0.25
P(2) = ___
p(3) = 2 * p(2) = 3 * p(4)
p(4) = ___
p(5) = ___
p(6) = ___

lands on 5 ten percent more often than it lands on 4

p(1) = 0.25
P(2) = ___
p(3) = 2 * p(2) = 3 * p(4)
p(4) = ___
p(5) = 1.05 * p(4)
p(6) = ___

and ten percent less often than it lands on 6.

p(1) = 0.25
P(2) = ___
p(3) = 2 * p(2) = 3 * p(4)
p(4) = ___
p(5) = 1.05 * p(4) = 0.90 * p(6)
p(6) = ___

One more important piece of information: p(1) +
p(2) + p(3) + p(4) + p(5) + p(6) = 1 -- It's a probability distribution!

Information is one thing. It is time to take an analysis step.
 
a dice is biased so that i lands on 1 one quarter of the time.
So P(1)= 0.25

it lands on 3 twice as often as it land on 2 and three times as often as it lands on 4.
So P(3)= 2P(2)= 3P(4)

it lands on 5 ten percent more often than it lands on 4 and ten percent less often than it lands on 6.
So P(5)= 1.1P(4)= .9P(6).
Those must add to 1 so P(1)+ P(2)+ P(3)+ P(4)+ P(5)+ P(6)= 0.25+ P(2)+ 2P(2)+ 2P(2)/3+ (11/10)(2/3)P(2)+ (11/9)(2/3)P(2)= 1. Solve that equation for P(2) and use that to determine P(6).

if i roll the dice 350 times, how often should i expect to roll a 6?

Please show how you worked it out! Thanks :)
 
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