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Popular Word Problems >

a card is drawn at random from a standard deck of cards what is the probability of getting a red card or a queen

Solution

a c a r d i s d r a w n a t r an d o m f ro m a s t an d a r d d ec k o f c a r d s w ha t i s t h e p ro babi l i t y o f g e tt in g a re d c a r d or a q u ee n

Solution

\frac{7}{13}

+1

Decimal

0.53846 \dots

Solution steps

Find the probability of getting a red card:

\frac{1}{2}

Find the probability of a queen:

\frac{1}{13}

Find the probability of getting a red card and a queen:

\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}

Popular Examples

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