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You are dealt one card from a 52-card deck. Find the probability that you are dealt a nine or a red card.

Solution

You are dealt one card from a 52-card deck. Find the probability that you are dealt a nine or a red card.

Solution

\frac{7}{13}

Solution steps

Find the probability of you are dealt a 9:

\frac{1}{13}

Find the probability of a red card:

\frac{1}{2}

Find the probability of you are dealt a 9 and a red card:

\frac{1}{26}

Use the Inclusion-Exclusion formula

P (X \lor Y) = P (X) + P (Y) - P (X \land Y)

= \frac{1}{13} + \frac{1}{2} - \frac{1}{26}

\frac{1}{13} + \frac{1}{2} - \frac{1}{26} = \frac{7}{13}

= \frac{7}{13}

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