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GREYUIT [131]
3 years ago
7

A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. If they randomly decide who will

watch the movie, what is the probability that there are at least 3 girls in the group that watch the movie? A. 0.018 B. 0.268 C. 0.536 D. 0.821
Mathematics
2 answers:
Eddi Din [679]3 years ago
6 0

Answer:

D. 0.821

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The combinations formula is important to solve this question:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Desired outcomes

The order is not important. For example, Elisa, Laura and Roze is the same outcome as Roze, Elisa and Laura. This is why we use the combinations formula.

At least 3 girls.

3 girls

3 girls from a set of 5 and 2 boys from a set of 3. So

C_{5,3}*C_{3,2} = 30

4 girls

4 girls from a set of 5 and 1 boy from a set of 3. So

C_{5,4}*C_{3,1} = 15

5 girls

5 girls from a set of 5

C_{5,5} = 1

D = 30+15+1 = 46

Total outcomes

5 from a set of 8. So

T = C_{8,5} = 56

Probability

P = \frac{D}{T} = \frac{46}{56} = 0.821

So the correct answer is:

D. 0.821

podryga [215]3 years ago
6 0

Answer:

I got answer choice D

Hope this helps :)

Step-by-step explanation:

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