Respuesta :
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 = [tex]^{52} C_{13}[/tex]
Number of ways to dealt 9 black cards = [tex]^{26}C_{9}[/tex]
And, the number of ways to dealt 4 red cards = [tex]^{26} C_{4}[/tex]
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) = [tex]\frac{^{26}C_{9}\times \ ^{26}C_{4} }{^{52}C_{13} }[/tex]
⇒ P(E) = [tex]\frac{\frac{26!26!}{9!4!17!22!} }{\frac{52!}{13!39!} }[/tex]
⇒ 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:
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