Can someone please make sure this Pre-Algebra problem is correct? I’m trying to help my younger brother with his homework, and I want to make sure it’s correct.

Question

Two cards are drawn at random from a normal deck of 52 cards and not replaced. What is the probability that both cards are red?

(A) 1/4

(B) 1/2

(C) 13/51

(D) 25/102

My brother and I both got (B) 1/2, would this be the correct answer?

Answer 1

No. Not correct. The critical statement is that the cards are not replaced.

Draw #1: There are 26 red cards and 52 total cards so the probability of drawing a red card is 26/52 or 1/2

Draw #2: You previously drew a card and (since we are talking the probability of drawing 2 red cards) we assume the card you drew was red. There are now 51 total cards and there are 25 red cards. So the probability of drawing a red card is 25/51.

The probability of BOTH events happening is the product of the two probabilities so (1/2)•(25/51) = 25/102

Answer 2

Pr(2 Reds) = 1/2 x 25/51 = 25/102

Pr(2 Reds) = Pr(1st Red) x Pr(2nd Red) = 26/52 x 25/51

= 1/2 x 25/51 = 25/102

half the deck is red, diamonds or hearts

that's 1/2 chance on the 1st card, 26 reds out of 52 cards

26/52 = 1/2

but without replacement it's down to (26-1)/(52-1) = 25/51

25 reds left out of 51 remaining cards.

then multiply those two probabilities to get the probability of 2 reds. 1/2 x 25/51 = 25/102

If it were with replacement, the odds of red on each draw would be 1/2. That might have thrown you off. But even then, the probability of 2 reds with replacement would be 1/2 x 1/2 = 1/4

D is correct for "without replacement"

A would have been correct for "with replacement"

B would have been correct for just one draw

C is a little enticing, as 13 is the total number of diamonds or hearts. but not red cards. red cards are 2 x 13 = 26 out of 52. 51 is what you're left with after the 1st draw.