SOLUTION: A school is divided into two parts. Upper school and lower school. Upper school has 300 boys and 200 girls. Lower School has 400 boys and 300 girls. A student is selected at ran

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Question 936452: A school is divided into two parts. Upper school and lower school.
Upper school has 300 boys and 200 girls.
Lower School has 400 boys and 300 girls.
A student is selected at random from the school.
If the first student comes from the lower school, a second student is selected at random from the upper school, if the first student comes from the upper school, a second student is selected at random from the lower school.
Find the probability that the second student will be a girl.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
"or" --> add probabilities
"&" = "and" --> multiply probabilities

L = lower
U = upper
G = girl
B = boy

We want 

P(L&G&G or L&B&G or U&G&G or U&B&G) =

P(L&G&G) + P(L&B&G) + P(U&G&G) + P(U&B&G)

P(L) = 1%2F2
P(U) = 1%2F2
P(G from U) = 200%2F500=2%2F5
P(B from U) = 300%2F500=3%2F5
P(G from L) = 300%2F700=3%2F7
P(B from L} = 400%2F700=4%2F7

P(L&G&G) = (1/2)(3/7)(2/5) =  6/70
P(L&B&G) = (1/2)(4/7)(2/5) =  8/70
P(U*G&G) = (1/2)(2/5)(3/7) =  6/70
P(U*B*G) = (1/2)(3/5)(3/7) =  9/70
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                    TOTAL  = 29/70

Edwin