Simple and Compound Event

Q. Two dice are thrown together. Let A be the event ‘getting 5 on the first die’ and B be the event ‘getting 3 on the second die’. Are the events A and B independent?

1. Yes
2. No

Q. Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?

1. {1, 6, 9}
2. {1, 5, 7}
3. {7, 0, 5}
4. {4, 8, 9}

Q.

Two natural numbers are chosen at random from the first one hundred natural numbers. The probability that the product of the chosen numbers is a multiple of 7 is.

1. $\frac{{14}_{C_1}\times {13}_{C_1}}{{100}_{C_2}}$

2. $\frac{{14}_{C_2}}{{100}_{C_2}}+\frac{{14}_{C_1}{13}_{C_1}}{{100}_{C_2}}$

3. $\frac{{14}_{C_1}{86}_{C_1}}{{100}_{C_2}}+\frac{{14}_{C_2}}{{100}_{C_2}}$

4. $\frac{{14}_{C_2}}{{100}_{C_2}}+\frac{7_{C_1}{14}_{C_1}}{{100}_{C_2}}$

Q.

Which of the following is/are the definition of a simple event?

1. An event which is simple to understand

2. An event which will has simple outcomes

3. An event which has no outcomes

4. An event which has all only one outcome associated with it

Q. For the random experiment of removing two balls from a bag containing 4 red, 1 green and 3 blue balls, which of the following ordered pairs is not a sample point?
(Here 'R', 'G', 'B' denote red, green and blue ball respectively.)

1. (R, B)
2. (B, B)
3. (G, R)
4. (G, G)

Q. A dice is rolled once. The following event is described.
A = {Getting 5 or 6}
Which of the following is the complement of A?

1. {1, 2, 5}
2. {1, 2, 3, 4}
3. {1, 2, 6}
4. {1, 2, 3}

Q. A dice is thrown once
A = {Getting 1, 2, 3, 4 or 5}
B = {Getting 4 or 5}
Then complement of B = {1, 2, 3}

1. False
2. True

Q. The number of ways in which we can get a sum of $11$ by throwing three dice is :

1. $8$
2. $56$
3. $45$
4. $27$