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Popular Word Problems >

You are dealt one card from a 52-card deck. Find the probability that you are dealt an ace or a black card.

Solution

Y o u a re d e a lt o n e c a r d f ro m a 52 - c a r d d ec k . F in d t h e p ro babi l i t y t ha t yo u a re d e a lt an a ce or a b l a c k c a r d .

Solution

\frac{7}{13}

+1

Decimal

0.53846 \dots

Solution steps

Find the probability of you are dealt an ace:

\frac{1}{13}

Find the probability of a black card:

\frac{1}{2}

Find the probability of you are dealt an ace and a black 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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