Probability

A bag contains 5 5 blue balls and 4 4 red balls. Two balls are drawn in succession without replacement. What is the probability that one ball is blue and the other is red?

5 9 \dfrac{5}{9} 25 324 \dfrac{25}{324} 5 18 \dfrac{5}{18} None of these.

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2 solutions

Case 1: First draw is blue and second draw is red.

P 1 = 5 9 × 4 8 = 5 18 P_1=\dfrac{5}{9} \times \dfrac{4}{8}=\dfrac{5}{18}

Case 2: First draw is red and second draw is blue.

P 2 = 4 9 × 5 8 = 5 18 P_2=\dfrac{4}{9} \times \dfrac{5}{8}=\dfrac{5}{18}

Thus, the probability is

P = P 1 + P 2 = 5 18 + 5 18 = 5 9 P = P_1 + P_2 = \dfrac{5}{18}+\dfrac{5}{18}=\dfrac{5}{9}

Denton Young
Jun 15, 2017

P(both red) = 4 / 9 3 / 8 = 3 / 18 4/9 * 3/8 = 3/18

P(both blue) = 5 / 9 4 / 8 = 5 / 18 5/9 * 4/8 = 5/18

P(one of each) = 1 ( 3 / 18 + 5 / 18 ) = 1 8 / 18 = 10 / 18 = 5 / 9 1 - (3/18 + 5/18) = 1 - 8/18 = 10/18 = 5/9

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