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

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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first ball drawn is a redball if thesecond ball drawn is yellow=7/12N(Y) = 5N(R) = 7N(Total) = 7+512N(Y) / N(Total)= 5/12= N(R) / N(Total)= 7/12= 5/12 x 7/12= 35/144= Pr(RnY)/P(Y)35/144 x 12/5Pr(R|Y) = 7/12Probabilitythat thefirst balldrawn is aredball if thesecondball drawn isyellow=7/12