Question

Five cards are dealt from a standard 52-card deck. What is the probability that we draw (a) 3 aces and 2 kings? (b) a "full house" (3 cards of one kind, 2 cards of another kind)?

Answer 1

Answer:  a) 9.23×10⁻⁶ and b) 0.00144

Step-by-step explanation:

Since we have given that

Number of cards = 52

a) Probability that we draw 3 aces and 2 kings.

As we know that

Number of aces = 4

Number of kings = 4

Number of cards drawn = 5

So, the probability becomes,

$\dfrac{^4C_3\times ^4C_2}{^{52}C_5}=\dfrac{24}{2598960}=9.23\times 10^{-6}$

(b) a "full house" (3 cards of one kind, 2 cards of another kind)

Since there are 13 sets of each type  and we have to select and 2 kinds of it, so, it becomes $2\times ^{13}C_2$

So, it becomes,

$\dfrac{2\times ^{13}C_2\times ^4C_3\times ^4C_2}{^{52}C_5}=\dfrac{24\times 156}{2598960}=\dfrac{3744}{2598960}=0.00144$

Hence, a) 9.23×10⁻⁶ and b) 0.00144