There are two boxes. The first box contains 4 red chips and 3 blue chips. The se
ID: 3202983 • Letter: T
Question
There are two boxes. The first box contains 4 red chips and 3 blue chips. The second box contains 1 red chips and 5 blue chips. First, a chip is selected from the first box and put into the second box; then a chip is selected from the second box. Let B_1 be the event that the chip selected from the first box is red. Let B_2 be the event that the chip selected from the first box is blue. Let A be the event that the chip selected from the second box is red. Find P(B_1), P(B_2), P(A), P(B_1|A), and P(B_2|A).Explanation / Answer
P(B1) = P(chip selected fro first box is red) = 4/(4+3) = 4/7 = 0.571
P(B2) = P(chip selected fro first box is blue) = 3/7 = 0.428
P(A) = P(B1)P(chip selected from second box is red/B1) +P(B2)* P(chip selected from second box is red/B2)
= 0.571*((1+1)/7) + 0.428*(1/7) = 0.224
P(B1/A) = P(B1 and A)/P(A) = 0.571*((1+1)/7) /0.224 = 0.728
P(B12/A) = P(B2 and A)/P(A) = 0.428*(1/7) /0.224 = 0.272