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?
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?
Let $E$ be the event in which the spokesperson will be a male and $F$ be the event in which the spokesperson will be over $35$ years of age.
Accordingly, $P ( E )=\frac{3}{5}$ and $P ( F )=\frac{2}{5}$
since there is only one male who is over $35$ years of age,
$P ( E \cap F)=\frac{1}{5}$
We know that $P ( E \cup F)= P ( E )+ P ( F )- P ( E \cap F )$
$\therefore P ( E \cup F )=\frac{3}{5}+\frac{2}{5}-\frac{1}{5}=\frac{4}{5}$
Thus, the probability that the spokesperson will either be a male or over $35$ years of age is $\frac{4}{5}$.
Similar Questions
For two given events $A$ and $B$, $P\,(A \cap B) = $
For two given events $A$ and $B$, $P\,(A \cap B) = $
- [IIT 1988]
Given two independent events $A$ and $B$ such that $P(A) $ $=0.3, \,P(B)=0.6$ Find $P(A$ and $B)$.
Given two independent events $A$ and $B$ such that $P(A) $ $=0.3, \,P(B)=0.6$ Find $P(A$ and $B)$.
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) = $
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) = $
For any two events $A$ and $B$ in a sample space
For any two events $A$ and $B$ in a sample space
- [IIT 1991]
True statement $A$ and true statement $B$ are two independent events of an experiment.Let $P\left( A \right) = 0.3$ , $P\left( {A \vee B} \right) = 0.8$ then $P\left( {A \to B} \right)$ is (where $P(X)$ denotes probability that statement $X$ is true statement)
True statement $A$ and true statement $B$ are two independent events of an experiment.Let $P\left( A \right) = 0.3$ , $P\left( {A \vee B} \right) = 0.8$ then $P\left( {A \to B} \right)$ is (where $P(X)$ denotes probability that statement $X$ is true statement)