1
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable has the following probability distribution

$\mathrm{X:}$ 0 1 2 3 4 5 6 7
$\mathrm{P}(x):$ 0 $\mathrm{2p}$ $\mathrm{2p}$ $\mathrm{3p}$ $\mathrm{p^2}$ $\mathrm{2p^2}$ $\mathrm{7p^2}$ $\mathrm{2p}$

Then the value of p is

A
$\frac{1}{10}$
B
$\frac{1}{30}$
C
$\frac{1}{100}$
D
$\frac{3}{20}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that A or B occurs is $\frac{1}{2}$, then the probability of both of them occur together is

A
0.1
B
0.2
C
0.01
D
0.02
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable $X$ has the following probability distribution

$\mathrm{X:}$ 1 2 3 4 5
$\mathrm{P(X):}$ $\mathrm{k^2}$ $\mathrm{2k}$ $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{5k^2}$

Then $\mathrm{P(X > 2)}$ is equal to

A
$\frac{7}{12}$
B
$\frac{23}{36}$
C
$\frac{1}{36}$
D
$\frac{1}{6}$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability, that a student will get 4 or more correct answers just by guessing, is

A
$\frac{10}{3^5}$
B
$\frac{17}{3^5}$
C
$\frac{13}{3^5}$
D
$\frac{11}{3^5}$
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