Question

two cards are drawn simultaneously from a well shuffled deck of 52 paying cards. find the probablity distribution of number of aces

Answer 1

The probability distribution of drawing aces from a deck can be represented by three probabilities: no aces drawn, exactly one ace drawn, and exactly two aces drawn, with respective calculations based on the number of aces and non-ace cards in the deck.

Step-by-step explanation:

To find the probability distribution of the number of aces drawn from a well-shuffled deck of 52 cards, we need to consider all possible scenarios: drawing 0 aces, 1 ace, or 2 aces.

• 0 aces: There are 4 aces in a deck, so there are 48 non-ace cards. The probability of drawing two non-aces is calculated by (48/52) * (47/51).
• 1 ace: The probability of drawing one ace and one non-ace can occur in two ways - first drawing an ace and then a non-ace, or first a non-ace then an ace. The combined probability is 2 * (4/52) * (48/51).
• 2 aces: The probability of drawing two aces is (4/52) * (3/51).

To summarize, the probability distribution is:

• P(0 aces) = (48/52) * (47/51)
• P(1 ace) = 2 * (4/52) * (48/51)
• P(2 aces) = (4/52) * (3/51)