12 yellow balls and 14 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?

Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/13

Number of yellow balls, N(Y) = 12

Number of red balls, N(R) = 14

Total number of balls, N(Total) = 12 + 14

N(Total) = 26

Probability of picking a yellow a ball

Pr(Y) = N(Y) / N(Total)

Pr(Y) = 12/26 = 6/13

Probability of picking a red ball

Pr(R) = N(R) / N(Total)

Pr(R) = 14/26 = 7/13

Probability of the two balls are red and yellow

Pr(RnY) = 6/13 x 7/13

Pr(RnY) = 42/169

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) = 42/169 ÷ 6/13

Pr(R|Y) = 42/169 x 13/6

Pr(R|Y) = 7/13

Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/13

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12 + 14 = 26 balls total

 probability of picking a red one first = 14/26 reduces to 7/13

 then a yellow ball second would be 12/25

 probability of both happening = 7/13 x 12/25 = 84/325

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