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91
MCQ (Single Correct Answer)

In a college, $30 \%$ students fail in Physics, $25 \%$ fail in Mathematics and $10 \%$ fail in both. One student is chosen at random. The probability that she fails in Physics, if she has failed in Mathematics is

A
$\frac{1}{10}$
B
$\frac{2}{5}$
C
$\frac{9}{20}$
D
$\frac{1}{3}$
92
MCQ (Single Correct Answer)

$A$ and $B$ are two students. Their chances of solving a problem correctly are $\frac{1}{3}$ and $\frac{1}{4}$, respectively. If the probability of their making a common error is, $\frac{1}{20}$ and they obtain the same answer, then the probability of their answer to be correct is

A
$\frac{1}{12}$
B
$\frac{1}{40}$
C
$\frac{13}{120}$
D
$\frac{10}{13}$
93
MCQ (Single Correct Answer)

If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement atmost one is defective?

A
$\left(\frac{9}{10}\right)^5$
B
$\frac{1}{2}\left(\frac{9}{10}\right)^4$
C
$\frac{1}{2}\left(\frac{9}{10}\right)^4$
D
$\left(\frac{9}{10}\right)^5+\frac{1}{2}\left(\frac{9}{10}\right)^4$
94

If $P(A)>0$ and $P(B)>0$. Then, $A$ and $B$ can be both mutually exclusive and independent.

A
TRUE
B
FALSE
95

If $A$ and $B$ are independent events, then $A^{\prime}$ and $B^{\prime}$ are also independent.

A
TRUE
B
FALSE
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