Drawing a card

Probability Level 2

A card is drawn at random from an ordinary deck of 52 52 playing cards. Find the probability that it is neither a club nor a four.

17 26 \dfrac{17}{26} 35 52 \dfrac{35}{52} 17 52 \dfrac{17}{52} 9 13 \dfrac{9}{13}

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1 solution

There are 13 clubs and 4 fours, but 1 four is also a club, therefore the desired probability is

P = 1 − ( 13 52 + 4 52 − 1 52 ) = 1 − 4 13 = P=1-\left(\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}\right)=1-\dfrac{4}{13}= 9 13 \color{#D61F06}\boxed{\dfrac{9}{13}}

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