1
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

A fair coin is tossed 100 times. The probability of getting a head for even number of times is

A
$$\frac{1}{2}$$
B
$$\frac{3}{8}$$
C
$$\frac{1}{8}$$
D
$$\frac{3}{4}$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the function defined by $$f(x)=K(x-x^2)$$ if $$0 < x < 1=0$$, otherwise is the p.d.f. of a r.v.X, then the value of $$P\left(X<\frac{1}{2}\right)$$ is

A
$$ \frac{1}{2} $$
B
$$ \frac{1}{3} $$
C
$$ \frac{1}{4} $$
D
$$ \frac{2}{3} $$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The probability distribution of the number of doublets in four throws of a pair of dice is given by

A
$$\mathrm{X}$$ 0 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$ $$\frac{1}{5}$$
B
$$\mathrm{X}$$ 0 1 2 3
$$\mathrm{P(X) :}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$
C
$$\mathrm{X}$$ 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$ $$\frac{1}{4}$$
D
$$\mathrm{X}$$ 0 1 2 3 4
$$\mathrm{P(X) :}$$ $$\frac{625}{1296}$$ $$\frac{125}{324}$$ $$\frac{25}{216}$$ $$\frac{5}{324}$$ $$\frac{1}{1296}$$
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

For the probability distribution given by following

$$\mathrm{x}$$ 5 6 7 8 9 10 11
$$\mathrm{P(X=x)}$$ 0.07 0.2 0.3 $$\mathrm{k}$$ 0.07 0.04 0.02

Var(X) =

A
2.65
B
2.85
C
1.65
D
3.85
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