A game comes with a deck of cards with each card showing one of the numbers...

A game comes with a deck of cards with each card showing one of the numbers 2, 3, 4, 5, 6, or 8. Each card occurs one time in red, one time in purple, and one time in blue. Given that a blue card is drawn, what is the probability the card is a 4?

Solutions

Expert Solution

Lets rephrase the conditions. There are 18 cards, 6 red ( 2,3,4,5,6,8), 6 purple ( 2,3,4,5,6,8), 6 blue ( 2,3,4,5,6,8). Please clarify in comments if this is not the case.

Assuming that above holds, we need to find the probability that drawn card is 4 given that a blue card is drawn.

By bayes theorem:-

P(Card is 2)=3/18

P(Card is 3)=3/18

P(Card is 4)=3/18

P(Card is 5)=3/18

P(Card is 6)=3/18

P(Card is 8)=3/18

P(Card is Blue | It is 2)=1/3

P(Card is Blue | It is 3)=1/3

P(Card is Blue | It is 4)=1/3

P(Card is Blue | It is 5)=1/3

P(Card is Blue | It is 6)=1/3

P(Card is Blue | It is 8)=1/3

Hence:-

orchestra answered 1 year ago

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