Question

A 13 card hand is dealt from a well-shuffled standard 52-card deck. What is the probability that 4 red cards and 9 black cards are dealt

Answer 1

The probability that 4 red cards and 9 black cards are dealt is 0.0735.

Let E be the event that 4 red cards and 9 black cards are dealt.

According to the given question.

Number of card hand that is dealt from a well-shuffled standard 52- card deck is 13

Total number of red cards in a well shuffled card deck = 26

Total number of black cards in a well shuffled card = 26

Now, the number of ways to dealt 13 cards = $^{52} C_{13}$

Number of ways to dealt 9 black cards = $^{26}C_{9}$

And, the number of ways to dealt 4 red cards = $^{26} C_{4}$

As, we know that the probability of an event is calculated by taking the ratio of the favorable outcomes to the total number of outcomes.

Therefore, the the probability that 4 red cards and 9 black cards are dealt is given by

P(E) = $\frac{^{26}C_{9}\times \ ^{26}C_{4} }{^{52}C_{13} }$

⇒ P(E) = $\frac{\frac{26!26!}{9!4!17!22!} }{\frac{52!}{13!39!} }$

⇒ P(E) = 0.0735

Hence, the probability that 4 red cards and 9 black cards are dealt is 0.0735.

Find out more information about probability here:

brainly.com/question/14530583

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