Question

Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a spade and the second card is red? (Round your answer to three decimal places.)

Answer 1

Answer:

The answer is 0.123.

Step-by-step explanation:

You want to find the intersection between P(Spade) and P(Red). Knowing that there's no replacement, the probability will be given by the formula:

⇒ P(Spade∩Red) = P(Spade)*P(Red/Spade)

⇒ P(Spade∩Red) = P(Red)*P(Spade/Red)

Either formula works, but I'm going to choose to work with the first formula.

Therefore:

P(Spade) = $\frac{13}{52}$

P(Red/Spade) =  $\frac{26}{52-1}$

So:

P(Spade∩Red) = $\frac{13}{52}$*$\frac{26}{51}$= $\frac{13}{102}$ =  $0.123$