Question

1. Suppose one basket has five white balls and seven black balls. A second basket has three white balls and twelve black balls. We will flip a fair coin and if it lands “heads” a ball from basket 1 is selected, and if it lands “tails” a ball from basket 2 is selected. Suppose that we have done this and that a white ball was selected, what is the probability that the coin landed tails？

Answer 1

probability of selecting white ball from basket 1 = $\frac{5}{5+7}=\frac{5}{12}$

probability of selecting white ball from basket 2 = $\frac{3}{3+12}=\frac{1}{5}$

probability that the coin landed tails =  $\frac{\frac{1}{5}}{\frac{5}{12}+\frac{1}{5}}=\frac{\frac{1}{5}}{\frac{37}{60}}=\frac{12}{37}$

Ans = 12/37

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