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Both red among the top two

EasyProbabilityConditional Probability & Expectation~3m

Two cards are dealt without replacement from a standard 52-card deck. Given that at least one of the two is red, what is the probability that both are red? Give your answer as a decimal (to 4 decimals).

Show hints (2)+
  1. Use P(both red∣at least one red)=P(both red)/P(at least one red)P(\text{both red}\mid\text{at least one red}) = P(\text{both red}) / P(\text{at least one red}).
  2. Get the conditioning event from its complement, "both black."

Answer

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0.3247 (± 0.001)

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Asked at: Game-Based Aptitude, Options Market-Making

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