A statistician is betting in a game of Counting Rates and Probability. The game uses cards,...

A statistician is betting in a game of Counting Rates and Probability. The game uses cards, but 1/3 of the cards are red, and 2/3 of the cards are black. If the statistician gets a red card his face will blush 30% of the time. If the statistician gets a black card his face will blush 60% of the time. Assuming you see the statisticians face blushing, what is the probability he just drew a black card?
Answer to 3 decimals

Expert Solution

P(red cards) = 1/3

P(black cards) = 2/3

P(face will blush | red card) = 0.3

P(face will blush | black card) = 0.6

P(face will blush) = P(face will blush | red card) * P(red card) + P(face will blush | black card) * P(black card)

= 0.3 * 1/3 + 0.6 * 2/3

= 0.5

P(black card | face blushing) = P(face will blush | black card) * P(black card) / P(face will blush)

= (0.6 * 2/3) / 0.5

= 0.8 (ans)

orchestra answered 2 years ago

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