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

Answer:

The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is $\frac{8}{5525}$

Step-by-step 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 $P_1=\frac{4}{52}$

Number of face cards = 12

Probability of getting a face card is $P_2=\frac{12}{51}$

Number of 10's = 4

Probability of getting a 10's is $P_3=\frac{4}{50}$

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

$P=P_1\times P_2\times P_3$

$P=\frac{4}{52}\times \frac{12}{51}\times \frac{4}{50}$

$P=\frac{1}{13}\times \frac{12}{51}\times \frac{2}{25}$

$P=\frac{8}{5525}$

Therefore, The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is $\frac{8}{5525}$