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Probability/Probability Distribution Watch

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    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)
    The answer is wrong.
    Thanks in advance for any help!
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    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.
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    (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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