Question

a card is drawn at random from a standard deck. that card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. what is the probability that all three of the cards are red? (if necessary, consult a list of formulas.)

Explanation:

Step1: Probability first red card

A standard deck has 52 cards, 26 red.
$\frac{26}{52}$

Step2: Probability second red card

Now 51 cards left, 25 red.
$\frac{25}{51}$

Step3: Probability third red card

Now 50 cards left, 24 red.
$\frac{24}{50}$

Step4: Multiply all probabilities

Find joint probability of all three events.
$\frac{26}{52} \times \frac{25}{51} \times \frac{24}{50}$

Step5: Calculate final value

Simplify and compute the product.
$\frac{26 \times 25 \times 24}{52 \times 51 \times 50} = \frac{15600}{132600} \approx 0.1176$

Answer:

0.1176