Question

Find the probability of drawing a red ace and then a spade when two cards are dranw (without replacement) from a standard deck of cards.a. 1/102b. 31/102c. 1/2d. 31/64

Answer 1

a. probability of drawing a red ace (first draw)

In a standard deck, there are 52 cards. Out of these 52 cards, two are red aces. Hence, the probability of drawing a red ace is 2/52 or 1/26.

b. probability of drawing a spade (second draw)

On the second draw, 51 cards are left. Assuming that a red ace was taken on the first draw, 13 spades are left on the deck. Hence, the probability of drawing a spade is 13/51.

So, to get the probability of drawing a red ace AND a spade, simply multiply the two probabilities above.

`(1)/(26)*(13)/(51)=(13)/(1326)`

Then, reduce 13/1326 into its simplest form by dividing both numerator and denominator by 13.

`(13/13)/(1326/13)=(1)/(102)`

Hence, the probability of drawing a red ace AND a spade is 1/102. (Option A)