# Mutually Exclusive Events

## Trending Questions

**Q.**

Three coins are tossed simultaneously. List the sample space for the event.

**Q.**

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination, is 0.02. Find the probability that

(i) both Anil and Ashima will not qualify the exam.

(ii) atleast one of them will not qualify the exam.

(iii) only one of them will qualify the exam.

**Q.**Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.

**Q.**

A, B, C are three mutually exclusive and exhaustive events associated with a random experiment.

If P(B)=(32)P(A) and P(C)=(12)P(B), find P(A).

**Q.**

Three groups of children contain 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys. One child is selected at random form each group. What is the chance that the three selected consist of 1 girl and 2 boys?

1732

1132

332

1332

**Q.**A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

**Q.**

If the probability of the occurrence of a certain event E is 311, find

(i) The odds in favour of its occurrence. and

(ii) The odds against its occurrence.

**Q.**Three coins are tossed. Describe (i) Two events which are mutually exclusive. (ii) Three events which are mutually exclusive and exhaustive. (iii) Two events, which are not mutually exclusive. (iv) Two events which are mutually exclusive but not exhaustive. (v) Three events which are mutually exclusive but not exhaustive.

**Q.**Given P(A) = and P(B) = . Find P(A or B), if A and B are mutually exclusive events.

**Q.**An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: A: the sum is greater than 8, B: 2 occurs on either die C: The sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive?

**Q.**25.Find the probability of having al least one boy in a family of 3 children

**Q.**34. What is the chance of getting 7 or 11 with two dice ?

**Q.**

If the odds in favour of an event be 33, find the probability of the occurrence of the event.

**Q.**1. A couple has three children . The probability of having 2sons and a daughter , if the eldest child is a son is ?.

**Q.**A bag contains 3 red, 4 white and 5 blue balls (All balls are different). If two balls are drawn at random, then the probability that they are of different colours is:

- 4766
- 1033
- 522
- None

**Q.**A card is picked from a well shuffled deck of 52 cards.if a face card comes up, then a die is rolled once and if a non face card comes up, then a coin is tossed. Find the probability of getting a perfect number on the die or a tail.

**Q.**

Let A, B and C be three events, if the probability of occuring exactly one event out of A and B is (1-x), out of B and C is (1-2x), out of C and A is (1-x) and that of occuring three events simultaneously is x^2, then prove that the probability that atleast one out of A, B and C will occut is greater than 12

**Q.**Three coins are tossed describe

(i) Two events which are mutually exclusive

(ii) Three events which are mutually exclusive and exhaustive

(iii) Two events which are not mutually exclusive

(iv) Two events which are mutually exclusive but not exhaustive

(v) Three events which are mutually exclusive but not exhaustive

**Q.**Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice ≤ 5 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) (iv) A and C are mutually exclusive (v) A and are mutually exclusive (vi) are mutually exclusive and exhaustive.

**Q.**A and B are two events such that P(A)=0.54, P(B)=0.69 and P(A ∩B) =0.35

Find (i) P(A∪B)

(ii) P(A' ∩B')

(iii) P(A ∩B')

(iv) P(B ∩A')

**Q.**

If m is a natural such that m≤5, then the probability that the quadratic equation x2+mx+12+m2=0 has real roots is

3/5

1/5

2/3

1

**Q.**81.Three symmetrical dices are thrown .The probability that the same number will appear on each of them is? options: (a)1/216 (b)1/36 (c)35/36 (d)1/35

**Q.**A player tosses a coin and scores one point for every head and two point for every tail that truns up. He plays on until his scores reaches or psses n. Pn denotes the probability of getting a scores of exactly n

List IList II(a) the value of Pn is (p) 1(b) the value of Pn+12Pn−1(q) 54(c) 2P101+P100(r) 2(d) P1+P2(s) 12[Pn−1+Pn−2]

Which of the following is the onlyincorrect option?

- (a)→(s)
- (c)→(q)
- (d)→(q)
- (b)→(p)

**Q.**2. Find the probability of getting one girl in a family of 3 children.

**Q.**In random experiment of rolling an unbiased die, let A be the event of getting a digit less than 4 and B be the event of getting a digit greater than 3 ; Show that the events A & B are mutually exclusive and exhaustive.

**Q.**Urn A contains 6 red, 4 white balls and urn B contains 4 red and 6 white balls. One ball is drawn at random from the urn A and placed in the urn B. Then one ball is drawn at random from the urn B and placed in the urn A. If one ball is now drawn from the urn A, the probability that it is found to be red is:

- 150
- 3255
- 3045
- 3250

**Q.**16 people study French, 21 study Spanish and total number of students studying these languages is 30. Consider the experiment of radomnly selecting students and the events X and Y defined as

X = {Student studying French is selected}

Y = {Student studying Spanish is selected}

X and Y are mutually exclusive events.

- True
- False

**Q.**Ques-1 Whats the probability of having 4 sons to a couple ? Ques-2 Whats the probability of having 3 daughters to a couple ?

**Q.**Let S be a sample space. A and B are two mutually exclusive events such that A∪B=S. If P(.) denotes the probability of the event, then the maximum value of P(A)P(B) is

**Q.**Two dice are thrown. The events A, B and C are as follows:

A : getting an even number on the first die

B : getting an odd number on the first die

C : getting the sum of the numbers on the dice ≤5

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