Question

Your cousin reaches into a bag that contains 12 popcorn balls 16 rice cakes, and 10granola bars. What is the probability that your cousin will pick a popcorn ball?Answer should be in simplified fraction form or decimal form rounded to the nearestwhole percent.

Answer 1

Given:

`\begin{gathered} N_{\text{umber of popcorn balls}}=12 \\ N_{\text{umber of rice cakes}}=16 \\ N_{\text{umber of granola bars}}=10 \end{gathered}`

To Determine: The probability that your cousin will pick a popcorn ball

Calculate the total of items in the bag

`T_{he\text{ total number of items in the bag}}=12+16+10=38`

The probability of an event A from a sample space S is given by the formula

`\begin{gathered} P_{\text{robability of event A}}=(n(A))/(n(S)) \\ N_{\text{umber of element in event A}}=n(A) \\ N_{\text{umber of element in the sample space}}=n(S) \end{gathered}`

Apply the probability formula to calculate the probability that your cousin will pick a popcorn ball as shown below

`\begin{gathered} P_{\text{robability }thatyourcousinwillpickapopcornball}=\frac{N_{umber\text{ of popcorn balls}}}{T_{otal\text{ number of items in the bag}}} \\ P_{\text{robability }thatyourcousinwillpickapopcornball}=(12)/(38) \\ P_{\text{robability }thatyourcousinwillpickapopcornball}=(6)/(19),or, \\ P_{\text{robability }thatyourcousinwillpickapopcornball}\approx32\% \end{gathered}`

Hence, the probability that your cousin will pick a popcorn ball is 6/19 or 32%