probability

[tltdas]

THank you so much for the help for my previous posting. I was able to use that formula with much ease. However, now I have another question. I do not think the previous way of doing it will work,and my book is NO HELP. Here is the question.

If 5 apples in a barrel of 25 are rotten, what is the expected number of rotten apples in a random sample of 2 apples?

 

[tkhunny]

5/25 = x/2

x is the expected value.

There are WAY more complicated ways to do it, if you like.

 

[arthur ohlsten]

the answer 2/5 is correct , but here is another derivation


5 bad 20 good

probability of 0 bad in choice of 2, P[0
P[0]= 20C2 5C0 / 25C2
P[0]= 20!/[2!18!][ 5!/0!5!]/ 25!/2!23!
P[0]=19/30

Probability of 1 bad
P[1]=20C1 5C1 / 25C2
P[1]=10/30

Probability of 2 bad P[2]
P[2]=20C0 5C2 / 25C2
P[2]= 1/30

If mean equals nP
mean = 0[19/30]+1[10/30]+2[1/30]
mean= 12/30 or 2/5

Arthur

 

[soroban]

Hello, tltdas!

TK and Arthur are absolutely correct . . . here's another approach.

If 5 apples in a barrel of 25 are rotten,
what is the expected number of rotten apples in a random sample of 2 apples?

There are four possible outcomes:

0 rotten: both are good.
. . . P(0 rotten) .= .(20/25)(19/24) .= .19/30

1 rotten, 1 good: in that order.
. . . P(1 rotten, 1 good) .= .(5/25)(20/24) .= .1/6

1 good, 1 rotten: in that order
. . . P(1 good, 1 rotten) .= .(20/25)(5/24) .= .1/6

2 rotten
. . . P(2 rotten) .= .(5/25)(4/24) .= .1/30


EV . = . 0(19/30) + 1(1/6) + 1(1/6) + 2(1/30) . = . 2/5

 

[Denis]

"If 5 apples in a barrel of 25 are rotten, what is the expected
number of rotten apples in a random sample of 2 apples?"

A bowl contains 5 red and 20 black jelly beans.
2 are pulled at random.
What is expected number of red jelly beans pulled?

 

[Gene]

I always have trouble with the concept. Isn't the

expected number of rotten apples in a random sample of 2 apples

0 rotten ones? I would have my flabber gasted if I got 2/5 of an apple. 19/30 is more than half so I would expect to get 2 good ones. Now if the question were "the average number"...
-----------------
Gene

 

[Matt]

I always have trouble with the concept. Isn't the

expected number of rotten apples in a random sample of 2 apples

0 rotten ones? I would have my flabber gasted if I got 2/5 of an apple. 19/30 is more than half so I would expect to get 2 good ones. Now if the question were "the average number"...

expected value = average number

 

[tkhunny]

flabber gasted if I got 2/5 of an apple

Expectation should not be assigned to a single experiment.

Agreed that there are many ways to say it poorly.