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Bob flips a fair coin. If Bob’s outcome is heads, Chuck draws a card randomly from a Poker deck where the four kings have been removed beforehand; If Bob’s outcome is tails, Chuck draws a card randomly from another Poker deck where the four aces have been removed beforehand. (There are 52 cards in a standard deck, among which there are 4 kings and 4 aces). Finally, if Chuck gets a king David raises a red flag; otherwise David raises a green flag. What is the probability that David raises a green flag?

User Martijno
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1 Answer

2 votes

Answer:

The probability is 0.9583

Explanation:

First, we have 2 possibilities, Bob's outcome is heads or Bob's outcome is tails.

If Bob's outcome is heads, the probability that Chuck doesn't get a king is equal 1, because there aren't kings in the poker deck. it means that if Bob's outcome is heads, the probability that David raises a green flag is 1.

On the other hand, if Bob's outcome is tails, the probability that Chuck doesn't get a king is equal to:


(44)/(48)=0.9166

Because there are 48 cards in the poker deck (without the 4 aces) and 44 of them aren't kings. So, if Bob's outcome is Tails, the probability that David raises a green flag is 0.9166.

Now, the probability that David raises a green flag is calculated as:


P=0.5(1)+0.5(0.9166)=0.9583

Because there is a probability of 0.5 that Bob's outcome is heads and there is a probability of 0.5 that Bob's outcome is Tails.

User Tudor Carean
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