1
COMEDK 2024 Morning Shift
+1
-0

The probability that a randomly chosen number from one to twelve is a divisor of twelve is

A
$$\frac{5}{12}$$
B
$$\frac{1}{3}$$
C
$$\frac{5}{6}$$
D
$$\frac{1}{2}$$
2
COMEDK 2024 Morning Shift
+1
-0

If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ then the possible values of $x$ lies in the interval

A
$$\left[\frac{1}{3}, \frac{2}{9}\right]$$
B
$$\left[-\frac{1}{3}, \frac{5}{9}\right]$$
C
$$[0,1]$$
D
$$\left[-\frac{7}{9}, \frac{4}{9}\right]$$
3
COMEDK 2024 Morning Shift
+1
-0

An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Otherwise it is replaced along with another ball of the same colour. The process is repeated. The probability that the third ball drawn is black is

A
$$\frac{17}{30}$$
B
$$\frac{37}{60}$$
C
$$\frac{31}{60}$$
D
$$\frac{23}{30}$$
4
COMEDK 2024 Morning Shift
+1
-0

A random variable X with probability distribution is given below

$$\mathrm{X}=x_i$$
2 3 4 5
$$\mathrm{P}\left(\mathrm{X}=x_i\right)$$
$$\frac{5}{k}$$
$$\frac{7}{k}$$
$$\frac{9}{k}$$
$$\frac{11}{k}$$

The mean of this distribution is

A
$$\frac{61}{16}$$
B
$$\frac{61}{8}$$
C
7
D
$$\frac{61}{4}$$
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