Respuesta :
Answer:
The probability is 0.000495
Step-by-step explanation:
As per the question:
Total no. of cards in a deck = 52
No. of spades in a deck = 13
Now, we have to select 5 cards in a deck such that they belong to the same suit, i.e., spades.
The no. of ways of selecting 5 cards from a deck = [tex]^{52}C_{5} = \frac{52!}{5!(52 - 5)!} = \frac{52!}{5!47!}[/tex]
The no. of ways of selecting 5 cards from 13 spade cards = [tex]^{13}C_{5} = \frac{13!}{5!(13 - 5)!} = \frac{13!}{5!8!}[/tex]
Now,
Probability that the selected 5 cards are all spades, P(E) = [tex]\frac{No.\ of\ ways\ of\ selecting\ 5\ cards\ from\ 13\ spade\ cards}{No.\ of\ ways\ of\ selecting\ 5\ cards\ from\ a\ deck}[/tex]
P(E) = [tex]\frac{^{13}C_{5}}{^{52}C_{5}}[/tex]
P(E) = [tex]\frac{\frac{13!}{5!8!}}{\frac{52!}{5!52!}}[/tex]
P(E) = [tex]\frac{\frac{13\times 12\times 11\tiems 10\times 9}{5\times 4\times 3\times 2\times 1}}{\frac{52\times 51\times 50\times 49\times 48}{5\times 4\times 3\times 2\times 1}}[/tex]
P(E) = [tex]\frac{13\times 12\times 11\tiems 10\times 9}{52\times 51\times 50\times 49\times 48} = 4.95\times 10^{- 4} = 0.000495[/tex]
