Question

multiple choice 1 point
you are dealt two cards successively without replacement from a standard deck of 52 playing cards. find the probability that the first card is a two and the second card is a ten. (round your answer to 3 decimal places)
0.500
0.094
0.250
0.006

Explanation:

1. First, calculate the probability of drawing a two - first:

• In a standard deck of 52 playing cards, there are 4 twos. So the probability of drawing a two as the first card, \(P(\text{first card is two})\), is \(\frac{4}{52}=\frac{1}{13}\).

1. Then, calculate the probability of drawing a ten as the second card given that the first card was a two:

• Since the first card was not replaced, there are now 51 cards left in the deck. There are 4 tens in a standard deck. So the probability of drawing a ten as the second card given that the first card was a two, \(P(\text{second card is ten}|\text{first card is two})\), is \(\frac{4}{51}\).

1. Use the multiplication rule for dependent - events:

• The probability that the first card is a two and the second card is a ten is \(P = P(\text{first card is two})\times P(\text{second card is ten}|\text{first card is two})\).
• Substitute the values: \(P=\frac{4}{52}\times\frac{4}{51}=\frac{16}{2652}\approx0.006\).

Answer:

0.006