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Probability/Probability Distribution watch

1. There are a large number of students in Luttley College. 60% of the students are boys. Students can choose exactly one of Games, Music or Drama. It is found that 75% of the boys choose Games, 10% of the boys choose Drama and the remainder of the boys choose Music. Of the girls, 30% choose Games, 55% choose Drama and the remainder choose Music.
5 Drama students are choose at random. Find the probability that at least 1 of them is a boy.

0.6x are boys. x is the total number of students.
0.1*0.6x are drama boys
1-P(X=0)
1-5C5(0.55)^5
=0.95 (approx)
Thanks in advance for any help!
2. I'll fix x as 100 for simplicity. The wording suggests the 5 students have to be all different, but you can't find a result if that were true. 6 boys choose drama, and 22 girls choose drama. (22/28)^5 is the chance that all 5 are girls selected with replacement. 1-(22/28)^5 is about 70%. It's not 0.55 since you're looking at the proportion of drama students who are girls, not the proportion of girls who are drama students.
3. (Original post by hrunting)
I'll fix x as 100 for simplicity. The wording suggests the 5 students have to be all different, but you can't find a result if that were true. 6 boys choose drama, and 22 girls choose drama. (22/28)^5 is the chance that all 5 are girls selected with replacement. 1-(22/28)^5 is about 70%. It's not 0.55 since you're looking at the proportion of drama students who are girls, not the proportion of girls who are drama students.
Ohhhh. I see. So I will have to use conditional probability and do the sum then, right?

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