1
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A random variable x has the following probability distribution. Then value of $k$ is _________ and $\mathrm{P}(3< x \leq 6)$ has the value

$\mathrm{X}=x$ 0 1 2 3 4 5 6 7 8
$\mathrm{P}(x)$ $\mathrm{k}$ $\mathrm{2k}$ $\mathrm{3k}$ $\mathrm{4k}$ $\mathrm{4k}$ $\mathrm{3k}$ $\mathrm{2k}$ $\mathrm{k}$ $\mathrm{k}$

A
$\frac{1}{20}, \frac{3}{7}$
B
$\frac{5}{21}, \frac{3}{7}$
C
$\frac{1}{21}, \frac{3}{7}$
D
$\frac{1}{20}, \frac{4}{7}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{X} \sim \mathrm{B}\left(6, \frac{1}{2}\right)$, then $\mathrm{P}[|x-4| \leqslant 2]$ is

A
$\frac{115}{128}$
B
$\frac{63}{64}$
C
$\frac{57}{64}$
D
$\frac{7}{64}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the number is odd, he loses an amount equal to the number shown. Then his expectation is ₹.

A
1
B
1.5
C
2
D
0.5
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Let X denote the random variable of number of jacks obtained in the two drawn cards. Then $P(X=1)+P(X=2)$ equals

A
$\frac{24}{169}$
B
$\frac{52}{169}$
C
$\frac{25}{169}$
D
$\frac{49}{169}$
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