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You are dealt one card from a 52-card deck. Find the probability that you are dealt a spade or a non dash picture card.

Solution

You are dealt one card from a 52-card deck. Find the probability that you are dealt a spade or a non dash picture card.

Solution

\frac{10}{13}

Solution steps

Find the probability of you are dealt a spade:

\frac{1}{4}

Find the probability of a non dash picture card:

\frac{9}{13}

Find the probability of you are dealt a spade and a non dash picture card:

\frac{9}{52}

Use the Inclusion-Exclusion formula

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

= \frac{1}{4} + \frac{9}{13} - \frac{9}{52}

\frac{1}{4} + \frac{9}{13} - \frac{9}{52} = \frac{10}{13}

= \frac{10}{13}

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