Exhaustive Events

Q.

Refer to question 6 above, state true or false (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B'
(iv) A and C are mutually exclusive
(v) A and B' are mutually exclusive
(vi) A' B', C are mutually exclusive and exhaustive.

Q.

How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once ?

Q. A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ .The probability of hitting the target $5^{th}$ time at the ${10}^{th}$ throw is

1. $\frac{{}^{10}{C}_4}{2^{10}}$
2. $\frac{63}{2^9}$
3. $\frac{{}^{10}{C}_5}{2^{10}}$
4. $\frac{5}{2^{10}}$

Q. A coin is tossed 3 times. Let the event A and B as
A: "At least one head."
B: "At least one tail."
Then both the events are mutually exclusive.

1. False
2. True

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. A batsman is going to face a delivery. Following events are described.
X = {He will get out}
Y = {He will score one or more runs on this delivery}
Z = {He will not score any run on this delivery}
Events X , Y and Z are exhaustive events.

1. True
2. False

Q.

A dice is rolled and two events P and Q are given as
P = {1, 4, 3, 5}, Q = {2, 6}

Which of the following describes the relation between P and Q?

1. Mutually exclusive events

2. Exhaustive events

3. Simple events

4. Compound events

Q. A sample space S is given as S = {1, 2, 3, 4, 5, 6, 7}
Following events are described for this sample space.
Event X = {1, 2, 3}
Y = {3, 4, 5}
Z = {5, 6, }
Events X , Y and Z are not exhaustive events because event X and event Y have an element in common

1. True
2. False