MATH SOLVE

2 months ago

Q:
# 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.)

Accepted Solution

A:

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 - 52Number of Ace = 4Probability of getting an ace is [tex]P_1=\frac{4}{52}[/tex]Number of face cards = 12Probability of getting a face card is [tex]P_2=\frac{12}{51}[/tex]Number of 10's = 4Probability 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]