Question

Three cards are dealt from a shuffled standard deck of playing cards.What is the probability that the three cards dealt are, in order, an ace, a face card, and a 6? (A face card is a jack, queen, or king.)

Answer 1

Let's calculate the probability of each card separately, then the final probability will be the product of each probability.

There are 4 ace cards in a deck of 52 cards, therefore the probability of picking an ace is 4/52.

Then, there are 12 face cards in a deck, but now the deck has only 51 cards (one already picked), so the probability is 12/51.

There are 4 cards numbered 6 in a deck, which now has 50 cards, so the probability is 4/50.

Then, the final probability is:

`\begin{gathered} P=(4)/(52)\cdot(12)/(51)\cdot(4)/(50) \\ P=(192)/(132600) \\ P=0.001448 \end{gathered}`

The probability is 0.001448.