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

The answer is 0.123.

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) =
`(13)/(52)`

P(Red/Spade) =
`(26)/(52-1)`

So:

P(Spade∩Red) =
`(13)/(52)`*
`(26)/(51)`=
`(13)/(102)` =
`0.123`