Question

Carl has a piece of toast that has jelly on one side, and he dropped it twice. Both times, it landed with the jelly side up. If he drops it 2 more times, what is the probability that it will have landed jelly side up a total of 3 times? (A) 1/4(B) 1/3(C) 1/2(D) 2/3

Answer 1

Option A -
`(1)/(4)`

Explanation:

Given : Carl has a piece of toast that has jelly on one side, and he dropped it twice. Both times, it landed with the jelly side up. If he drops it 2 more times.

To find : What is the probability that it will have landed jelly side up a total of 3 times?

Solution :

Carl has a piece of toast which is two sided.

Probability of success is
`p=(1)/(2)`

He drop the piece 4 times so n=4

The probability that it will have landed jelly side up a total of 3 times is given by binomial probability distribution.

i.e.
`P(X=r)=^nC_r* p^r* (1-p)^(n-r)`

Here, r=3

`P(X=3)=^4C_3* ((1)/(2))^3* (1-(1)/(2))^(4-3)`

`P(X=3)=(4!)/(3!(4-3)!)* ((1)/(2))^3* ((1)/(2))^(1)`

`P(X=3)=4* ((1)/(2))^4`

`P(X=3)=(1)/(4)`

Therefore, The probability that it will have landed jelly side up a total of 3 times is
`(1)/(4)`

So, Option A is correct.