Question

Find P (Junior|Girl) Hint: P(A and B)

Answer 1

Answer:  1/6

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Explanation:

There are two methods to approach this type of problem.

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Method 1

A = junior

B = girl

P(A) = probability of selecting a junior

P(B) = probability of selecting a girl

P(B) = (number of girls)/(number total)

P(B) = (4+7+3+4)/(4+4+5+7+2+3+1+4)

P(B) = 18/30

P(B) = 9/15

P(A and B) = probability of selecting a girl who is a junior

P(A and B) = (number of girl juniors)/(number total)

P(A and B) = 3/30

P(A and B) = 1/10

P(A given B) = P(A and B)/P(B)

P(A given B) = (1/10) divided by (9/15)

P(A given B) = (1/10) times (15/9)

P(A given B) = (1*15)/(10*9)

P(A given B) = 15/90

P(A given B) = 1/6

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Method 2

This method doesn't involve dividing two fractions which could get messy, which is why I find this the easier route. Since we are given the person is a girl, this means we only need to focus on the "girls" column. There are 3 who are juniors out of 4+7+3+4 = 18 total. The probability of selecting a girl junior is 3/18 = 1/6