MCQ

MCQ 11 Mark

If $A$ and $B$ are events such that $P(A)=0.2, P(B)=$ 0.4 and $P(A \cup B)=0.5$, the value of $P\left(\frac{A}{B}\right)$ is

A
0.1
✓
0.25
C
0.5
D
0.08

Answer

Correct option: B.

0.25

(b) 0.25
Explanation : Given, $P(A)=0.2, P(B)=0.4$ and $P(A \cup B)=0.5$
We know that,
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\therefore \quad P(A \cap B)=0.2+0.4-0.5$
or, $\quad P(A \cap B)=0.1$
Now, $\quad P\left(\frac{A}{B}\right)=\frac{P(A \cap D)}{P(B)}=\frac{0.1}{0.4}=0.25$.

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MCQ 21 Mark

If $P(A)=\frac{1}{2}, P(B)=0$, then $P\left(\frac{A}{B}\right)$ is

A
0
B
$\frac{1}{2}$
✓
not defined
D
1

Answer

Correct option: C.

not defined

(c) not defined
Explanation : Given, $P(A)=\frac{1}{2}$ and $P(B)=0$
$\because \quad P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}$
$\Rightarrow \quad P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{0}$
$=\infty$ (not defined).

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MCQ 31 Mark

If $P\left(\frac{A}{B}\right)>P(A)$, then which of the following is correct :

A
$P\left(\frac{B}{A}\right) < P(B)$
B
$P(A \cap B) < P(A) \cdot P(B)$
✓
$P\left(\frac{B}{A}\right)>P(B)$
D
$P\left(\frac{B}{A}\right)=P(B)$

Answer

Correct option: C.

$P\left(\frac{B}{A}\right)>P(B)$

(c) $P\left(\frac{B}{A}\right)>P(B)$
Explanation : Given, $P\left(\frac{A}{B}\right)>P(A)$
$\Rightarrow \quad \frac{P(A \cap B)}{P(B)}>P(A)$
$\Rightarrow \quad P(A \cap B)>P(A) \cdot P(B)$
$\Rightarrow \quad \frac{P(A \cap B)}{P(A)}>P(B)$
$\Rightarrow \quad P\left(\frac{B}{A}\right)>P(B)$

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MCQ 41 Mark

If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P\left(\frac{B}{A}\right)=1$, then

✓
$A \subset B$
B
$B \subset A$
C
$B=\phi$
D
$A=\phi$

Answer

Correct option: A.

$A \subset B$

(a)$A \subset B$
Explanation : $P(A) \neq 0$ and $P\left(\frac{B}{A}\right)=1$
$\because \quad P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)}$
$\therefore \quad 1=\frac{P(A \cap B)}{P(A)}$
$\Rightarrow \quad P(A)=P(A \cap B)$
$\therefore \quad A \subset B$.

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