SOLUTION: Two cards are randomly selected from a standard 52-card deck. what is the probability of getting 2 hearts or 2 numbers less than 8?

Question 243587: Two cards are randomly selected from a standard 52-card deck. what is the probability of getting 2 hearts or 2 numbers less than 8?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two cards are randomly selected from a standard 52-card deck. what is the probability of getting 2 hearts or 2 numbers less than 8?
P(2 hearts) = 13C2/52C2
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P(2 numbers less than 8) = 28C2/52C2
Note: I'm assuming the ace is less than 8.
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P(2 hearts AND less than 8) = 14C2/52C2
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Your Problem:
P(2 hearts OR 2 numbers less than 8) = P(2 hearts)+P(2 less than 8)
- P(2 hearts AND 2 less than 8)
= [13C2 + 28C2 - 14C2]/52C2
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= [365]/1326
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= 0.27526...
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Cheers,
Stan H.
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