SOLUTION: Out of 20 girls in a class, 12 like music and 15 like movie.IF a girl is selected at random from the class, what is the probability that she likes both lobbies?

Question 1024056: Out of 20 girls in a class, 12 like music and 15 like movie.IF a girl is selected at random from the class, what is the probability that she likes both lobbies?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
Out of 20 girls in a class, 12 like music and 15 like movie.IF a girl is selected at random from the class, what is the probability that she likes both lobbies?

Solution:
We're missing some information here.
There are 20 girls in the class, out of which 12 like music and 15 like movie.
It is not stated how many of them like neither music or movie. This number could range from 0 to 5 (since 15 like movie).
To answer the question, we take two extreme cases.
(a) Every girl likes either movie or music, or both.
This means that 15 like movie, the remaining five like only music. That leave 7 who like both.
(b) Five (maximum) girls don't like movie, nor music.
That leaves all 12 girls who like music like movie as well.

Therefore the number of girls who like both music and movie ranges from 7 to 12.
Hence the probability of a randomly selected girl liking both is 7/20 to 12/20, or between 0.35 and 0.60.
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