Question

5 yellow balls and 7 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow

Answers

  1. Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12
    Number of yellow balls, N(Y) = 5
    Number of red balls, N(R) = 7
    Total number of balls, N(Total) = 7+5
    N(Total) = 12
    Probability of picking a yellow a ball
    Pr(Y) = N(Y) / N(Total)
    Pr(Y) = 5/12
    Probability of picking a red ball
    Pr(R) = N(R) / N(Total)
    Pr(R) = 7/12
    Probability of the two balls are red and yellow
    Pr(RnY) = 5/12 x 7/12
    Pr(RnY) = 35/144
    Probability that the first ball drawn is a red ball if the second ball drawn is yellow
    Pr(R|Y) = Pr(RnY)/P(Y)
    Pr(R|Y) = 35/144 ÷ 5/12
    Pr(R|Y) = 35/144 x 12/5
    Pr(R|Y) = 7/12
    Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12
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