Answer:
(a) Probability = 0.29947
Step-by-step explanation:
The probability of the hand containing exactly one ace would be:
Number of ways this can happen = 4C1 * 48C4 (using combinations)
Number of ways this can happen = 4 * 194580
Number of ways this can happen = 778,320
Total number possible hands = 2,598,960 (as stated in question)
Total probability of exactly one ace = Number of ways to get an ace / total number of ways
Total probability = 778320 / 2598960 = 0.29947
Thus, the probability of the hand containing exactly one ace will be 0.2994
Another way to solve this:
Probability of one ace and 5 other cards = [tex]\frac{4}{52}*\frac{48}{51}*\frac{47}{50}*\frac{46}{49}*\frac{45}{48}[/tex] = 0.059894
Number of ways to arrange 1 ace and 4 other cards = 5
Total probability = 0.0598 * 5 = 0.29947
