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14.Probability
easy
If $A$ and $B$ an two events such that $P\,(A \cup B) = \frac{5}{6}$,$P\,(A \cap B) = \frac{1}{3}$ and $P\,(\bar B) = \frac{1}{3},$ then $P\,(A) = $
A
$\frac{1}{4}$
B
$\frac{1}{3}$
C
$\frac{1}{2}$
D
$\frac{2}{3}$
Solution
(c) $P(A) = P(A \cap B) + P(A \cup B) – P(B)$
$ = \frac{1}{3} + \frac{5}{6} – \frac{2}{3} = \frac{3}{6} = \frac{1}{2}.$
Standard 11
Mathematics
Similar Questions
From the employees of a company, $5$ persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows :
S.No. | Name | Sex | Age in years |
$1.$ | Harish | $M$ | $30$ |
$2.$ | Rohan | $M$ | $33$ |
$3.$ | Sheetal | $F$ | $46$ |
$4.$ | Alis | $F$ | $28$ |
$5.$ | Salim | $M$ | $41$ |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over $35$ years?
medium