Question

If you are dealt 5 cards at random from a standard deck of playing cards, what is the probability that at most 4 of them are spades?

Answer 1

Answer:

Step-by-step explanation:

No of ways in which 5 cards are chosen is $N=^{52}C_5$

No of ways in which at most  4 cards are spades $N_0=$Total ways-5 spades

$=^{52}C_5-^{13}C_5$

Probability that at most 4 cards are spade $P=\frac{N_0}{N}$

$P=\frac{^{52}C_5-^{13}C_5}{^{52}C_5}$

$P=\frac{2598960-1287}{2598960}$

$P=\frac{2597673}{2598960}=0.9995$