One card is drawn from a pack of 52 cards. probability that it is a queen or heart is

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Gujarati

Hindi

14.Probability

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One card is drawn from a pack of $52$ cards. The probability that it is a queen or heart is

A

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

B

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

C

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

D

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

Solution

(c) Probability that it is queen $P(A) = \frac{4}{{52}} = \frac{1}{{13}}$

Probability that it is heart $P(B) = \frac{{13}}{{52}} = \frac{1}{4}$

Probability that it is queen and heart $P(A \cap B) = \frac{1}{{52}}$

$\therefore $ $P$ (Queen or heart) $ = P(A) + P(B) – P(A \cap B)$

$ = \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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