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Popular Word Problems >

Suppose you draw one card from a standard 52-card deck. What is the probability that it is a red or a Jack?

Solution

S u pp ose yo u d r a w o n e c a r d f ro m a s t an d a r d 52 - c a r d d ec k . Wha t i s t h e p ro babi l i t y t ha t i t i s a re d or a J a c k ?

Solution

\frac{7}{13}

+1

Decimal

0.53846 \dots

Solution steps

Find the probability of it is a red:

\frac{1}{2}

Find the probability of a jack:

\frac{1}{13}

Find the probability of it is a red and a jack:

\frac{1}{26}

Use the Inclusion-Exclusion formula

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

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

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

= \frac{7}{13}

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