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

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) (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

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

Use a calculator.....

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

RELATED QUESTIONS
Three cards are drawn without replacement from an ordinary deck of 52 playing cards. A... (answered by Edwin McCravy)

2. if each card in a standard 52 card deck of playing cards has the same probability of (answered by duotmto)

2. if each card in a standard 52 card deck of playing cards has the same probability of... (answered by stanbon)

from a deck of 52 ordinary playing cards, 2 cards are drawn without replacement. find the (answered by stanbon)

1. Two cards are selected without replacement from a usual deck of 52 cards. [A deck of... (answered by stanbon)

A standard deck of 52 playing cards will have cards in fours suits (clubs, diamonds,... (answered by checkley79)

3. From a deck of 52 ordinary playing cards, two cards are drawn with replacement. Find... (answered by Photonjohn)

A single card is drawn from a standard 52-deck of cards with four suits: hearts, clubs,... (answered by Edwin McCravy)

Consider a standard deck of 52 cards having 13 clubs, 13 diamonds, 13 hearts, and 13... (answered by galactus)