Question

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?

Answer 1

Combination is a way of selecting random number of people, items, etc. from a collection without minding the order of the selection.

If 5 tickets out of 8 friends wherein at least 3 girls in the group will watch the movie then:
8C5 (number of friends who will watch the movie) - 5C3 (at least 3 girls will watch)= 46

The probability that at least 3 girls in the group will watch the movie is: 46/56= 0.82143

Answer 2

The total number of ways 5 people can be selected out of 8 is 8C5 (combination of 8 taken 5) which is equal to 56. Given the conditions that at least three girls should watch the movie.
(1) girls - 3 ; boys - 2 ; (5C3) x (3C2) = 30
(2) girls - 4 ; boy - 1 ; (5C4) x (3C1) = 15
(3) girls - 5 ; boy - 0 ; (5C5) x (3C0) = 1

Adding all the three possibilities, 46. The probability is the ratio of this value and the total number, 56. Thus, the answer is approximately 0.80.