a regular deck of cards has 52 cards with 4 aces. carl asked a friend to pick a card from the deck three…

a regular deck of cards has 52 cards with 4 aces. carl asked a friend to pick a card from the deck three times, replacing the card each time. his friend picked three aces. which expression will give the probability of that event?

a regular deck of cards has 52 cards with 4 aces. carl asked a friend to pick a card from the deck three times, replacing the card each time. his friend picked three aces. which expression will give the probability of that event?

Answer

Explanation:

Step1: Calculate the probability of picking an ace first time

The probability of picking an ace from a deck of 52 cards is $\frac{4}{52}$ (since there are 4 aces in a deck of 52 cards).

Step2: Calculate the probability of picking an ace second time

After picking one ace, there are 3 aces left and 51 cards left. So the probability is $\frac{3}{51}$.

Step3: Calculate the probability of picking an ace third time

After picking two aces, there are 2 aces left and 50 cards left. So the probability is $\frac{2}{50}$.

Step4: Calculate the compound probability

Since these are dependent events (the outcome of the first pick affects the second, and so on), we multiply the probabilities of each individual event. So the probability is $(\frac{4}{52})(\frac{3}{51})(\frac{2}{50})$.

Answer:

$(\frac{4}{52})(\frac{3}{51})(\frac{2}{50})$