SOLUTION: In a standard deck of 52 playing cards, two cards are known: the 2 of hearts, and the 2 of clubs. If four cards are drawn from the remaining 50 cards in the deck, without replac

Algebra ->  Probability-and-statistics -> SOLUTION: In a standard deck of 52 playing cards, two cards are known: the 2 of hearts, and the 2 of clubs. If four cards are drawn from the remaining 50 cards in the deck, without replac      Log On


   

Question 1162210: In a standard deck of 52 playing cards, two cards are known: the 2 of hearts, and the 2 of clubs.
If four cards are drawn from the remaining 50 cards in the deck, without replacement, what is the probability that at least one of the cards is a club OR a heart?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are 50 cards remaining, of which 26 are spades or diamonds and 24 are hearts or clubs.

Four cards are drawn from these 50 remaining cards, without replacement.

We want to find the probability of getting at least one club or one heart.

The opposite of getting at least one club OR one heart is getting no clubs AND no hearts. So the probability of getting at least one club OR one heart is 1 minus the probability of getting no clubs AND no hearts -- i.e., 1 minus the probability that all four cards are spades or diamonds.

The probability that, out of the 50 remaining cards, we pick 4 of the 26 that are spades or diamonds, is

C%2826%2C4%29%2FC%2850%2C4%29

So the probability that we get at least one heart OR one club is

1+-+C%2826%2C4%29%2FC%2850%2C4%29

Use a calculator.....

My calculator shows a probability between 93% and 94%.