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One card is selected at random from a standard 52-card deck. Find the probability the selected card is a Jack (J) or a red card. Give your answer as a decimal rounded to 4 decimal places.

Solution

One card is selected at random from a standard 52-card deck. Find the probability the selected card is a Jack ( J ) or a red card. Give your answer as a decimal rounded to 4 decimal places.

Solution

\frac{7}{13}

Solution steps

Find the probability of the selected card is a jack ( J ):

\frac{1}{13}

Find the probability of a red card.:

\frac{1}{2}

Find the probability of the selected card is a jack ( J ) 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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