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One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 4 or a spade.

Solution

One card is selected at random from a deck of cards. Determine the probability of selecting a card that is less than 4 or a spade.

Solution

\frac{19}{52}

Solution steps

Find the probability of selecting a card that is less than 4:

\frac{2}{13}

Find the probability of a spade:

\frac{1}{4}

Find the probability of selecting a card that is less than 4 and a spade:

\frac{1}{26}

Use the Inclusion-Exclusion formula

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

= \frac{2}{13} + \frac{1}{4} - \frac{1}{26}

\frac{2}{13} + \frac{1}{4} - \frac{1}{26} = \frac{19}{52}

= \frac{19}{52}

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