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 10? (A face card is a jack, queen, or king.)

Answer 1

The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is
`(8)/(5525)`

Explanation:

Given : Three cards are dealt from a shuffled standard deck of playing cards.

To find : What is the probability that the three cards dealt are, in order, an ace, a face card, and a 10? (A face card is a jack, queen, or king.)

Solution :

Total number of cards - 52

Number of Ace = 4

Probability of getting an ace is
`P_1=(4)/(52)`

Number of face cards = 12

Probability of getting a face card is
`P_2=(12)/(51)`

Number of 10's = 4

Probability of getting a 10's is
`P_3=(4)/(50)`

The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is give by

`P=P_1* P_2* P_3`

`P=(4)/(52)* (12)/(51)* (4)/(50)`

`P=(1)/(13)* (12)/(51)* (2)/(25)`

`P=(8)/(5525)`

Therefore, The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is
`(8)/(5525)`