One card is drawn randomly from a pack of 52 cards, then probability that it is a king or spade is

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14.Probability

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One card is drawn randomly from a pack of $52$ cards, then the probability that it is a king or spade is

A

$\frac{1}{{26}}$

B

$\frac{3}{{26}}$

C

$\frac{4}{{13}}$

D

$\frac{3}{{13}}$

Solution

(c) Probability of king $P(A) = \frac{4}{{52}} = \frac{1}{{13}}$

Probability of spade $ = \frac{{13}}{{52}}$ $ = \frac{1}{4}$

$\therefore$ $P$ (King or spade) $= P($king) $+ P$ (spade) $ – P$(King and spade)

$ = \frac{1}{{13}} + \frac{1}{4} – \frac{1}{{52}}$

$ = \frac{{4 + 13 – 1}}{{52}} = \frac{{16}}{{52}} = \frac{4}{{13}}$.

Standard 11

Mathematics

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