1
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
$$\frac{23}{30}$$
2
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
$$\frac{61}{4}$$
3
COMEDK 2023 Morning Shift
+1
-0

A number $$\mathrm{n}$$ is chosen at random from $$s=\{1,2,3, \ldots, 50\}$$. Let $$\mathrm{A}=\{n \in s: n$$ is a square $$\}$$, $$\mathrm{B}=\{n \in s: n$$ is a prime$$\}$$ and $$\mathrm{C}=\{n \in s: n$$ is a square$$\}$$. Then, correct order of their probabilities is

A
$$p(A) < p(B) < p(C)$$
B
$$p(A) > p(B) > p(C)$$
C
$$p(\mathrm{~B}) < p(\mathrm{~A}) < p(C)$$
D
$$p(A) > p(c) > p(B)$$
4
COMEDK 2023 Morning Shift
+1
-0

A five-digits number is formed by using the digits $$1,2,3,4,5$$ with no repetition. The probability that the numbers 1 and 5 are always together, is

A
$$\frac{2}{5}$$
B
$$\frac{1}{5}$$
C
$$\frac{3}{5}$$
D
$$\frac{1}{4}$$
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