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Tuesday, September 16, 2008

Q) There are 3 groups.The 1st group contains 3 girls & and 1 boy. The 2nd group contains 2 girls and 2 boys and the 3rd group contains 1 girl and 3 boys. Another group is formed by picking one student each from the existing groups. What is the probability that the group formed will contain 1 boy & 2 girls?

A)
The 3 groups are A, B and C.
The prob. we have to find is of getting BGG where B is boy and G is girl.

Case 1 - boy is selected from A, and the girls from B and C.
prob. of BGG = 1/4*1/2*1/4 = 1/32

Case 2 - boy is selected from B, and girls from A and C.
prob. of BGG = 1/2*3/4*1/4 = 3/32

Case 3 - boy is selected from C, and girls from A and B.
prob. of BGG = 3/4*3/4*1/2 = 9/32

Total prob. = Sum of prob.= 1/32 + 3/32 + 9/32
= 13/32

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