Respuesta :
Answer:
Option A - [tex]\frac{1}{4}[/tex]
Step-by-step 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 [tex]p=\frac{1}{2}[/tex]
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. [tex]P(X=r)=^nC_r\times p^r\times (1-p)^{n-r}[/tex]
Here, r=3
[tex]P(X=3)=^4C_3\times (\frac{1}{2})^3\times (1-\frac{1}{2})^{4-3}[/tex]
[tex]P(X=3)=\frac{4!}{3!(4-3)!}\times (\frac{1}{2})^3\times (\frac{1}{2})^{1}[/tex]
[tex]P(X=3)=4\times (\frac{1}{2})^4[/tex]
[tex]P(X=3)=\frac{1}{4}[/tex]
Therefore, The probability that it will have landed jelly side up a total of 3 times is [tex]\frac{1}{4}[/tex]
So, Option A is correct.
