Question

question 25
ahmad buys a bag of cookies that contains 6 chocolate - chip cookies, 4 peanut - butter cookies, 4 sugar cookies and 5 oatmeal cookies. what is the probability that ahmad randomly selects a chocolate - chip cookie from the bag, eats it, then randomly selects an oatmeal cookie?
probability = (round your answer to 4 decimal places.)

Explanation:

Step1: Calculate total number of cookies initially

The total number of cookies in the bag initially is $6 + 4+5=15$ cookies.

Step2: Calculate probability of first - selecting a chocolate - chip cookie

The probability of randomly selecting a chocolate - chip cookie first is $P(\text{chocolate chip})=\frac{6}{15}$.

Step3: Calculate number of cookies left after first selection

After eating the chocolate - chip cookie, the number of cookies left in the bag is $15 - 1=14$ cookies.

Step4: Calculate probability of second - selecting an oatmeal cookie

The probability of randomly selecting an oatmeal cookie second, given that a chocolate - chip cookie was selected first, is $P(\text{oatmeal}|\text{chocolate chip})=\frac{5}{14}$.

Step5: Calculate the joint probability

By the multiplication rule for conditional probability $P(A\cap B)=P(A)\times P(B|A)$, the probability of selecting a chocolate - chip cookie first and then an oatmeal cookie is $P=\frac{6}{15}\times\frac{5}{14}=\frac{30}{210}\approx0.1429$.

Answer:

$0.1429$