Question

here is a table showing all 52 cards in a standard deck.
suppose a card is drawn at random from a standard deck. the card is then shuffled back into the deck. then for a second time a card is drawn at random from the deck. the card is then shuffled back into the deck. finally, for a third time a card is drawn at random from the deck.
what is the probability of first drawing a face card, then a four, and then a red card?
do not round your intermediate computations. round your final answer to four decimal places.
(if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate face card probability

There are 12 face cards (Jack, Queen, King in 4 suits) in 52 cards.
$P(\text{face card}) = \frac{12}{52}$

Step2: Calculate four card probability

There are 4 fours (one per suit) in 52 cards.
$P(\text{four}) = \frac{4}{52}$

Step3: Calculate red card probability

There are 26 red cards (Hearts + Diamonds) in 52 cards.
$P(\text{red card}) = \frac{26}{52}$

Step4: Multiply independent probabilities

Since draws are with replacement, events are independent. Multiply the three probabilities.
$P(\text{combined}) = \frac{12}{52} \times \frac{4}{52} \times \frac{26}{52}$

Step5: Simplify and compute value

First simplify the product:
$\frac{12 \times 4 \times 26}{52 \times 52 \times 52} = \frac{12 \times 4}{2 \times 52 \times 52} = \frac{48}{5408} = \frac{3}{338}$
Calculate decimal value: $\frac{3}{338} \approx 0.0089$

Answer:

0.0089