Question

What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck?

Answer 1

94/54145 Would be your answer, hope this helps! :D

Answer 2

Answer:

Probability is 0.0017

Step-by-step explanation:

To find : The theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck

Solution :

$^nC_r=\frac{n!}{r!(n-r)!}$

Selecting 5 cards from deck of 52 cards is

$^{52}C_5=\frac{52!}{5!(52-5)!}$

$^{52}C_5=\frac{52\times51\times50\times49\times48\times47!}{5\times4\times3\times2\times1(47)!}$

$^{52}C_5=\frac{311875200}{120}=2598960$

Ways to get 3  4's is

$^{4}C_3=\frac{4!}{3!(4-3)!}$    

$^{4}C_3=\frac{4\times3!}{3!\times1}$

$^{4}C_3=4$          

Ways to get rest 2 cards from 48 cards is

$^{48}C_2=\frac{48!}{2!(48-2)!}$      

$^{48}C_2=\frac{48\times47\times46!}{2\times1\times46!}$

$^{48}C_2=1128$    

Probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck is

$P=\frac{^{4}C_3\times^{48}C_2}{^{52}C_5}$

$P=\frac{4\times1128}{2598960}$

$P=0.0017$

Therefore, The theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52-card deck is 0.0017.