Question

A cookie jar contains 8 oatmeal, 7 peanut butter and 10 sugar cookies. What is theprobability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls asugar cookie from the jar?A. 17/49B.7/60C. 17/600D. 7/600

Answer 1

B. 7/60

Step-by-step explanation:

Given;

Number of oatmeal cookies = 8

Number of peanut butter cookies = 7

Number of sugar cookies = 10

Total number of cookies = 8 + 7 + 10 = 25

So the probability of Ivan pulling a peanut butter cookie from the jar can be determined as seen below;

`\begin{gathered} P(\text{peanut butter cookie) }=\frac{\text{ number of peanut butter cookies}}{\text{Total number of cookies}} \\ P(\text{peanut butter cookie) }=(7)/(25) \end{gathered}`

So if Ivan ate the peanut butter cookie he pulled (he did not replace it), it means that the total number of cookies will be 24, so the probability of pulling a sugar cookie from the jar will now be;

`\begin{gathered} P(sugar\text{ cookie) }=\frac{\text{ number of sugar cookies}}{\text{Total number of cookies}} \\ P(sugar\text{ cookie) }=(10)/(24)=(5)/(12) \end{gathered}`

So we can determine the probability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls a sugar cookie from the jar by multiplying the above probabilities;

`P(peanut,sugar)=(7)/(25)*(5)/(12)=(7)/(5)*(1)/(12)=(7)/(60)`

Therefore, the probability is 7/60