Question

ahmed buys a bag of cookies that contains 9 chocolate chip cookies, 5 peanut butter cookies, 9 sugar cookies and 6 oatmeal cookies. what is the probability that ahmed reaches in the bag and randomly selects 2 sugar cookies from the bag? round your answer to four decimal places.

Explanation:

Step1: Calculate total number of cookies

The total number of cookies is $9 + 5+9 + 6=29$ cookies.

Step2: Calculate the number of ways to choose 2 sugar - cookies

The number of ways to choose 2 sugar - cookies out of 9 sugar - cookies is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 9$ and $r = 2$. So $C(9,2)=\frac{9!}{2!(9 - 2)!}=\frac{9\times8}{2\times1}=36$.

Step3: Calculate the number of ways to choose 2 cookies out of all cookies

The number of ways to choose 2 cookies out of 29 cookies is $C(29,2)=\frac{29!}{2!(29 - 2)!}=\frac{29\times28}{2\times1}=406$.

Step4: Calculate the probability

The probability $P$ of choosing 2 sugar - cookies is the number of favorable outcomes (choosing 2 sugar - cookies) divided by the number of total outcomes (choosing 2 cookies out of all cookies). So $P=\frac{C(9,2)}{C(29,2)}=\frac{36}{406}\approx0.0887$.

Answer:

$0.0887$