Answer:
The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is [tex]\frac{8}{5525}[/tex]
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 [tex]P_1=\frac{4}{52}[/tex]
Number of face cards = 12
Probability of getting a face card is [tex]P_2=\frac{12}{51}[/tex]
Number of 10's = 4
Probability of getting a 10's is [tex]P_3=\frac{4}{50}[/tex]
The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is give by
[tex]P=P_1\times P_2\times P_3[/tex]
[tex]P=\frac{4}{52}\times \frac{12}{51}\times \frac{4}{50}[/tex]
[tex]P=\frac{1}{13}\times \frac{12}{51}\times \frac{2}{25}[/tex]
[tex]P=\frac{8}{5525}[/tex]
Therefore, The probability that the three cards dealt are, in order, an ace, a face card, and a 10 is [tex]\frac{8}{5525}[/tex]
