If A and B are mutually exclusive events, then: - Vidyadip

MCQ

If $A$ and $B$ are mutually exclusive events, then:

✓
$\text{P(A)}\leq\text{P}(\bar{\text{B}})$
B
$\text{P(A)}\geq\text{P}(\bar{\text{B}})$
C
$\text{P}(\text{A})<\text{P}(\bar{\text{B}})$
D
none of these.

✓

Answer

Correct option: A.

$\text{P(A)}\leq\text{P}(\bar{\text{B}})$

For mutually exclusive events,
$\text{P}(\text{A}\cap\text{B})=0$
$\therefore\ \text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}$ $\big[\because\text{ P}(\text{A}\cap\text{B})=0\big]$
$\Rightarrow\text{P}(\text{A})+\text{P(B)}\leq1$
$\Rightarrow\text{P(A)}+1-\text{P}(\bar{\text{B}})\leq1$ $\big[\text{P(B)}=1-\text{P}(\bar{\text{B}})\big]$
$\Rightarrow\text{P(A)}-\text{P}(\bar{\text{B}})\leq0$
$\Rightarrow\text{P(A)}-\text{P}(\bar{\text{B}})$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The number of $4-$letter words, with or without meaning, each consisting of $2$ vowels and $2$ consonants, which can be formed from the letters of the word $UNIVERSE$ without repetition is $.........$.

Suppose ${A_1},\,{A_2},\,{A_3},........,{A_{30}}$ are thirty sets each having $5$ elements and ${B_1},\,{B_2}, ......., B_n$ are $n$ sets each with $3$ elements. Let $\bigcup\limits_{i = 1}^{30} {{A_i}} = \bigcup\limits_{j = 1}^n {{B_j}} = S$ and each elements of $S$ belongs to exactly $10$ of the $A_i's$ and exactly $9$ of the $B_j's$. Then $n$ is equal to

If $\cos\text{x}=-\frac{1}{2}$ and $0<\text{x}<2\pi,$ then the solutions are:

Equation of the line which passes through the point $( - 4,\;3)$ and the portion of the line intercepted between the axes is divided internally in the ratio $5 : 3$ by this point, is

In a non$-$leap year, the probability of having $53$ tuesdays or $53$ wednesdays is:

If $(p$ or $q)$ is true, then:

Let $f(x)=\sin \left(\frac{\pi}{6} \sin \left(\frac{\pi}{2} \sin x\right)\right)$ for all $x \in R$ and $g(x)=\frac{\pi}{2} \sin x$ for all $x \in R$. Let (f० g)(x) denote $f(g(x))$ and $(g \circ f)(x)$ denote $g(f(x))$. Then which of the following is (are) true ?

$(A)$ Range of $f$ is $\left[-\frac{1}{2}, \frac{1}{2}\right]$

$(B)$ Range of $f \circ g$ is $\left[-\frac{1}{2}, \frac{1}{2}\right]$

$(C)$ $\lim _{x \rightarrow 0} \frac{f(x)}{g(x)}=\frac{\pi}{6}$

$(D)$ There is an $x \in R$ such that $( g \circ f )(x)=1$

The geometric series $a + ar + ar^2 + ar^3 +..... \infty$ has sum $7$ and the terms involving odd powers of $r$ has sum $'3'$, then the value of $(a^2 -r^2)$ is -

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers. Let $f ( x )=\alpha x ^{5}+\beta x ^{3}+\gamma x , x \in R \quad$ and $\quad g : R \rightarrow R$ be such that $g(f(x))=x$ for all $x \in R$. If $a_{1}, a_{2}, a_{3}, \ldots, a_{n}$ be in arithmetic progression with mean zero, then the value of $f\left(g\left(\frac{1}{n} \sum_{i=1}^{n} f\left(a_{i}\right)\right)\right)$ is equal to.

If $a_1, a_2...,a_n$ an are positive real numbers whose product is a fixed number $c$ , then the minimum value of $a_1 + a_2 +.... + a_{n - 1} + 2a_n$ is