1
MHT CET 2023 9th May Morning Shift
+2
-0

The probability mass function of random variable X is given by

$$P[X=r]=\left\{\begin{array}{ll} \frac{{ }^n C_r}{32}, & n, r \in \mathbb{N} \\ 0, & \text { otherwise } \end{array} \text {, then } P[X \leq 2]=\right.$$

A
$$\frac{1}{3}$$
B
$$\frac{1}{2}$$
C
$$\frac{1}{4}$$
D
$$\frac{1}{5}$$
2
MHT CET 2023 9th May Morning Shift
+2
-0

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the uppermost faces, is

A
0.7
B
0.75
C
0.65
D
0.62
3
MHT CET 2021 21th September Evening Shift
+2
-0

an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. The probability that the three balls have difference colours is

A
$$\frac{1}{14}$$
B
$$\frac{3}{14}$$
C
$$\frac{1}{7}$$
D
$$\frac{2}{7}$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that at least 5 of them will be solved is

A
$$\frac{19}{1024}$$
B
$$\frac{19}{4096}$$
C
$$\left(\frac{1}{4}\right)^6$$
D
$$\frac{19}{2048}$$
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