1
MHT CET 2021 23th September Morning Shift
+2
-0

A random variable X has the following probability distribution

$$x$$ 0 1 2 3 4 5 6 7 8
$$P(X=x)$$ K 2K 3K 4K 4K 3K 2K K K

Then $$\mathrm{P}(3<\mathrm{x} \leq 6)=$$

A
$$\frac{3}{7}$$
B
$$\frac{4}{7}$$
C
$$\frac{13}{21}$$
D
$$\frac{8}{21}$$
2
MHT CET 2021 23th September Morning Shift
+2
-0

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

A
$$\frac{8}{19} \times \frac{7}{18}$$
B
$$\frac{8}{19}$$
C
$$\frac{8}{19} \times \frac{7}{19}$$
D
$$\frac{7}{18}$$
3
MHT CET 2021 22th September Evening Shift
+2
-0

The distribution function $$F(X)$$ of discrete random variable $$X$$ is given by

$$\mathrm{X}$$ 1 2 3 4 5 6
$$\mathrm{F (X=x)}$$ 0.2 0.37 0.48 0.62 0.85 1

Then $$\mathrm{P[X=4]+P[x=5]=}$$

A
0.14
B
0.85
C
0.37
D
0.23
4
MHT CET 2021 22th September Evening Shift
+2
-0

First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one ball is red and the other is black, is

A
$$\frac{41}{80}$$
B
$$\frac{21}{40}$$
C
$$\frac{3}{20}$$
D
$$\frac{3}{8}$$
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