Question

Bert and Ernie each have a well-shuffled standard deck of 52 cards. They each draw one card from their own deck. Compute the probability that neither bert nor ernie draws an ace.

Answer 1

The probability that neither Bert nor Ernie draws an ace from separate standard decks of cards is approximately 71.63%, calculated by multiplying the chance that each one draws a non-ace card (48/52) independently.

Step-by-step explanation:

To calculate the probability that neither Bert nor Ernie draws an ace from their own well-shuffled standard deck of 52 cards, we can use the complement rule. Firstly, there are 4 aces in a deck, so there are 52 - 4 = 48 cards that are not aces. We want to find the probability that both Bert and Ernie draw one of these 48 cards.

The probability that Bert draws a non-ace card is 48/52, since there are 48 non-ace cards out of the total 52 cards. Similarly, the probability that Ernie also draws a non-ace card is 48/52. Since Bert and Ernie have separate decks, these events are independent, and the probability that both events happen is the product of the individual probabilities.

Therefore, the probability that neither Bert nor Ernie draws an ace is:

P(Bert draws non-ace) × P(Ernie draws non-ace)= (48/52) × (48/52)= 0.8462 × 0.8462≈ 0.7163

This means there is approximately a 71.63% chance that neither Bert nor Ernie will draw an ace.