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probabilty of coosing 4 hearts in a row out of a standard deck of 52 cards

Asked Feb 10, 2012, 10:16 AM — 1 Answer

Four cards are chosen from a standard deck of 52 playing cards with replacement. What is the probability of choosing 4 hearts in a row

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ebaines Posts: 8,515, Reputation: 4904

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Feb 10, 2012, 11:40 AM

Here's how to approach this problem:

When you draw the first card there are 13 hearts in the deck out of 52 cards, so the probability of drawing a heart is 13/52. If you are succesful in drawing a heart, there are now 12 hearts left in a deck of 51 cards, and so the probability of drawing a second heart is 12/51. The probability that you draw a heart on both the first and second draws is therefore:

$<br /> P(2 \ hearts) = \frac {13} {52} \times \frac {12} {51}<br />$

Continuing on - the probability of drawing a third heart after you've already gotten the first two is 11/50. So the probability fo drawing three hearts in a row is:

$<br /> P(3 \ hearts) = \frac {13} {52} \times \frac {12} {51} \times \frac {11} {50}<br />$

Can you take it from here?

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