SOLUTION: Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond? What are the odds against getting a

Question 278057: Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond?

What are the odds against getting all heads or all tails in three successive flips of a coin?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing a club and a diamond?
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To get the odds against you need the probability for and the probability
against.
--
P(club and diamond) = (13/52)(13/51)
P(not drawing a club and a diamond) = 1 - (13^2/(52*51)) = (52*51-13^2)/(52*51)
-
---
Then odds against = P(against)/P(for) = (52*51-13^2)/13^2 = 2483:169
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What are the odds against getting all heads or all tails in three successive flips of a coin?
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P(all heads) = 1/8
P(all tails) = 1/8
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Assuming these events are independent you get:
P(all heads and all tails) = (1/8)^2 = 1/64
P(not) = 1-(1/64) = 63/64
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Then odd against = P(not)/P(for) = 63/1 = 63:1
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Cheers,
Stan H.

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