Question

If Bag A has 3 red and 3 green balls, and Bag B has 4 red and 6 green balls, if one ball is randomly selected from each bag, what is the probability that the balls are the same color? a) 1/2 b) 1/4 c) 5/18 d) 4/9

Answer 1

Answer: 1/2

Work Shown

P(2 red) = P(red from A and red from B)

P(2 red) = P(red from A)*P(red from B)

P(2 red) = (3/6)*(4/10)

P(2 red) = 12/60

P(2 red) = 1/5

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P(2 green) = P(green from A and green from B)

P(2 green) = P(green from A)*(P green from B)

P(2 green) = (3/6)*(6/10)

P(2 green) = 18/60

P(2 green) = 3/10

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P(2 same color) = P(2 red or 2 green)

P(2 same color) = P(2 red) + P(2 green)

P(2 same color) = 1/5 + 3/10

P(2 same color) = 2/10 + 3/10

P(2 same color) = (2+3)/10

P(2 same color) = 5/10

P(2 same color) = 1/2 is the final answer