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Answer :
Answer:
22.73% possibility that both of the scoops are ice cream
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order of the scoops is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the possibility that both of the scoops are ice cream?
Desired outcomes:
2 scoops of ice cream(set of 6). So
[tex]D = C_{6,2} = \frac{6!}{2!4!} = 15[/tex]
Total outcomes:
2 scoops from a set of 6 + 6 = 12. So
[tex]T = C_{12,2} = \frac{12!}{2!10!} = 66[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{15}{66} = 0.2273[/tex]
22.73% possibility that both of the scoops are ice cream
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