Mathematics, 16.09.2019 15:10 christiancase06

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?

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Answer from: edna27

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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Answer from: merzedes

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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Answer from: Quest

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