Card probability

Question

find the probability of selecting two 10s when two cards are drawn without replacement from a standard deck of cards

Answer 1

A = picking a first 10 from a standard deck of cards

B = picking a second 10 from a standard deck of cards

There are 52 cards in a standard deck. There are 4 cards that have a "10".

P(A ∩ B) = P(A)*P(B) = (4/52)*(3/51) = 0.004525

The probability of selecting two 10s from a standard deck of cards is about 0.004525.

Answer 2

There are 4 10's in a 52 card deck. The probability of drawing the first 10 is 4/52 = 1/13, leaving 51 cards and 3 10's. The probability of drawing the second 10 is 3/51 = 1/17. The probability of both events happening is 1/13 * 1/17 = 1/221.

Answer 3

Question: Find the probability of selecting two 10s when two cards are drawn without replacement from a standard deck of cards

Answer: Remember that we have 52 cards, four of which have "10" on them. Also, remember than in sampling without replacement, our sample size will decrease.

Probability of getting a 10-card: 4/52. Great. But what happens when we remove a card, and it happens to be a 10? Now there will be three 10-cards left in a stack of 51 cards.

(4/52)(3/51) = 1/221.