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 what is the probability that there are at least 3 girls in the group that watch the movle?

53.57%

Step-by-step explanation:

We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :

# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)

 = 10 * 3 = 30

That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.

# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56

That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:

P (3 girls and 2 boys) = 30/56 = 0.5357

Which means that the probability is 53.57%

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