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?\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{52}\\right)$\n$\\left(\\frac{1}{52}\\right)\\left(\\frac{1}{51}\\right)\\left(\\frac{1}{50}\\right)$\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{51}\\right)\\left(\\frac{4}{50}\\right)$\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{3}{51}\\right)\\left(\\frac{2}{50}\\right)$

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?\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{52}\\right)$\n$\\left(\\frac{1}{52}\\right)\\left(\\frac{1}{51}\\right)\\left(\\frac{1}{50}\\right)$\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{4}{51}\\right)\\left(\\frac{4}{50}\\right)$\n$\\left(\\frac{4}{52}\\right)\\left(\\frac{3}{51}\\right)\\left(\\frac{2}{50}\\right)$

Answer

Explanation:

Step1: Calculate first - pick probability

Since there are 4 aces in 52 cards, the probability of picking an ace on the first pick is $\frac{4}{52}$.

Step2: Calculate second - pick probability

Because the card is replaced, the deck remains the same. So the probability of picking an ace on the second pick is also $\frac{4}{52}$.

Step3: Calculate third - pick probability

Again, due to replacement, the probability of picking an ace on the third pick is $\frac{4}{52}$.

Step4: Calculate joint probability

For independent events (since the card is replaced each time), the joint probability is the product of the individual probabilities. So the probability of picking three aces is $\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$.

Answer:

$\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)\left(\frac{4}{52}\right)$