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14.Probability
medium
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
Similar Questions
Fill in the blanks in following table :
| $P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
| $\frac {1}{3}$ | $\frac {1}{5}$ | $\frac {1}{15}$ | …….. |
easy
