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Popular Word Problems >

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

O n e c a r d i s se l ec t e d a t r an d o m f ro m a s t an d a r d 52 - c a r d d ec k . F in d t h e p ro babi l i t y t h e se l ec t e d c a r d i s a J a c k (J) or a re d c a r d . G i v e yo u r an s w er a s a d ec ima l ro u n d e d t o 4 d ec ima l pl a ces .

Solution

\frac{7}{13}

+1

Decimal

0.53846 \dots

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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