Match probability questions with answers ( attached to details of this question. Will answer your question/ 10 points?

Assuming there are 52 cards in the deck.

1.

The probability of drawing a red ace is 2/52.

The probability of then drawing an ace of any colour is 3/51. This is because there are only 51 cards left since you already took out a red ace, and there are only 3 aces left too.

So the total probability of both these events happening is:

2/52 x 3/51 = 1/442

2.

The probability of drawing a 3 is 4/52, and the probability of drawing a 5 is 4/52. So the probability of drawing a 3 OR a 5 is:

4/52 + 4/52 = 8/52 = 2/13

Note the question says "with replacement", meaning you put the card back for your next go. The chance of getting a 4 is 4/52, and 6 is 4/52, so the chance of getting a 6 or 4 is 8/52 or 2/13 again.

The chance of both these events:

2/13 x 2/13 = 4/169

3.

Chance of drawing king is 4/52. Chance of drawing queen is 4/52. Total chance:

4/52 x 4/52 = 1/169

4.

Chance of drawing a spade is 13/52 = 1/4. Chance of a Jack is 4/52 = 1/13. Total chance:

1/4 x 1/13 = 1/52

So D.

The probability of drawing a red ace followed by another ace of any color without replacement.

In a fresh deck of cards, there are 2 red aces out of 52 cards total, so the probability of drawing one is 2/52 or 1/26.

With that ace gone from the deck, there are three aces remaining out of the remaining 51 cards, so the probability of drawing a second ace in this case is 3/51 or 1/17.

the probability of both events happening is the same as the product of the two individual probabilities, so:

1/26 * 1/17 = 1/442 or 0.00226 (to 3SF)

answer B.