For any two events $A$ and $B$ in a sample space
For any two events $A$ and $B$ in a sample space
- [IIT 1991]
- A
$P\,\left( {\frac{A}{B}} \right) \ge \frac{{P(A) + P(B) - 1}}{{P(B)}},\,\,P(B) \ne 0$ is always true
- B
$P\,(A \cap \bar B) = P(A) - P(A \cap B)$ does not hold
- C
$P\,(A \cup B) = 1 - P(\bar A)\,P(\bar B),$ if $A$ and $B$ are disjoint
- D
None of these
Similar Questions
If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $
If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $
One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent ?
$\mathrm{E}:$ ' the card drawn is black '
$\mathrm{F}:$ ' the card drawn is a king '
One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent ?
$\mathrm{E}:$ ' the card drawn is black '
$\mathrm{F}:$ ' the card drawn is a king '
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?
Events $E$ and $F$ are such that $P ( $ not $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.
Events $E$ and $F$ are such that $P ( $ not $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is
- [IIT 1992]