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 thedeck. 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 the first card drawn is a two, the second card drawn is a two, and the third card drawn is a face card?Do not round your intermediate computations. Round your final answer to four decimal places.

Answer 1

0.0011

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total Outcome

Since there are 52 cards in a deck, hence;

Total outcome = 52

If a two is drawn first, the probability of drawing a two is 4/52

Since it is not replaced, the total cards will become 51

If another two is drawn, the probability of drawing another two will be 4/51

If the third card drawn is a face, the probability of drawing a face = 12/50 (Since there are 12 faces)

The probability that the first card drawn is a two, the second card drawn is a two, and the third card drawn is a face card = 4/52 * 4/51 * 12/50

Hence the probability that the first card drawn is a two, the second card drawn is a two, and the third card drawn is a face card = 0.0011.