Question
A bag contains 6 red, 10 yellow, and 14 black balls. If
2 balls are picked at random without replacement, find the probability that the first ball is red and the second ball is either yellow or black.Solution
We have a bag with: 6 Red balls 10 Yellow balls 14 Black balls Total balls = 30 We pick two balls without replacement, and we need the probability that: First ball is Red. Second ball is either Yellow or Black. Step 1: Probability of picking a Red ball first First ball is Red. Second ball is either Yellow or Black. Probability of picking a Red ball first P(R1) = 6/30 = 1/5 Probability of picking a Yellow or Black ball next After picking a red ball, 29 balls remain. Yellow + Black balls left = 10+14 = 24. P(Y2 or B2) = 24/29 Multiply the probabilities P(R1 and (Y2 or B2)) = 1/5 × 24/29 = 24/145
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