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

In a Binomial distribution with $$\mathrm{n}=4$$, if $$2 \mathrm{P}(\mathrm{X}=3)=3 \mathrm{P}(\mathrm{X}=2)$$, then the variance is

A
$$\frac{36}{169}$$
B
$$\frac{144}{169}$$
C
$$\frac{9}{169}$$
D
$$\frac{16}{169}$$
2
MHT CET 2023 9th May Morning Shift
+2
-0

$$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ are three events, one of which must and only one can happen. The odds in favor of $$\mathrm{A}$$ are $$4: 6$$, the odds against $$B$$ are $$7: 3$$. Thus, odds against $$\mathrm{C}$$ are

A
$$7: 3$$
B
$$4: 6$$
C
$$6: 4$$
D
$$3: 7$$
3
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
$$\frac{1}{5}$$
4
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
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