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In 5-card poker, find the probability of being dealt the following hand. Refer to thetable. Note that a standard deck of playing cards has 52 cards—4 suits (clubs,diamonds, hearts, spades), where each suit has 13 cards (Ace, 2,3,4,5,6,7,8,9. 10. Jack Queen King).four fives

In 5card poker find the probability of being dealt the following hand Refer to thetable Note that a standard deck of playing cards has 52 cards4 suits clubsdiam class=

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ANSWER:

0.00001847

STEP-BY-STEP EXPLANATION:

A hand consists of 5 cards from a well shuffled deck of 5 cards.

Which means that there is a total number of outcomes = 52C5

[tex]\begin{gathered} _{52}C_5=\frac{52!}{5!\cdot47!} \\ \\ _{52}C_5=2598960 \end{gathered}[/tex]

Since we get 4 fives, number of favorable outcomes of a it would be 48 (52 - 4)

Therefore, the required probability is:

[tex]\begin{gathered} p=\frac{\text{ number of favorable outcomes}}{\text{ total number of outcomes }} \\ \\ \text{ we replacing:} \\ \\ p=\frac{48}{2598960}=0.00001846892\cong0.00001847 \end{gathered}[/tex]

The probability of being dealt four fives is 0.00001847

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