Question

#3 We draw the top 8 cards from a well-shuffled standard 52-card deck. nd the probability that: (a) The 8 cards include exactly 3 aces. (b) The 8 cards include exactly 2 kings. (c) The probability that the 8 cards include exactly 3 aces, or exactly 2 kings, or both. Fi

Answer 1

No of ways 8 cards can be picked up from 52 cards, N = 52C8

(a)

Total no of aces in a card pack = 4

Desired Probability = (4C3) * (48C5) / 52C8 = 9.1e-03

(b)

Total no of aces in a card pack = 4

Desired Probability = (4C2) * (48C6) / 52C8 = 0.09784

(c)

Desired Probability

$= \frac{4C3*48C5 + 4C2*48C6 + 4C3*4C2*44C3}{52C8} = 0.1074$

** If this answer does not match please comment.