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 :

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.

[tex]\frac{1}{26}\times\frac{13}{51}=\frac{13}{1326}[/tex]

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

[tex]\frac{13\div13}{1326\div13}=\frac{1}{102}[/tex]

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