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Popular Word Problems >

What is the probability of getting either a club or a jack when drawing a single card from a deck of 52 cards?

Solution

Wha t i s t h e p ro babi l i t y o f g e tt in g e i t h er a c l u b or a ja c k w h e n d r a w in g a s in g l e c a r d f ro m a d ec k o f 52 c a r d s ?

Solution

\frac{4}{13}

+1

Decimal

0.30769 \dots

Solution steps

Find the probability of getting either a club:

\frac{1}{4}

Find the probability of a jack when drawing a single card from a deck of 52 cards:

\frac{1}{13}

Find the probability of getting either a club and a jack when drawing a single card from a deck of 52 cards:

\frac{1}{52}

Use the Inclusion-Exclusion formula

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

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

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

= \frac{4}{13}

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