# Mutually Exclusive Events

## Trending Questions

**Q.**

A rifleman is firing at a distant target and has only $10\%$ chance of hitting it. The minimum number of round he must fire in order to have $50\%$chance of hitting it at least once i

$7$

$8$

$9$

$6$

**Q.**Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.12. Then the probability that neither A nor B occurs is:

- 0.13
- 0.37
- 0.63
- 0.38

**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 onlycorrect option?

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

**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.**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.**

A die is rolled. Let us define event E1 as the set of possible outcomes where the number on the face of the die is even and event E2 as the set of possible outcomes where the number on the face of the die is odd. Event E1 and E2 are mutually exclusive.

- True
- False

**Q.**

A man firing at a distant target has 10% chance of hitting the target in one shot. The number of times he must fire at the target to have about 50% chance of hitting the target is

$10$

$9$

$7$

$8$

**Q.**Two dice are rolled. Let us define the following events

A: "sum of numbers on dice is greater than

or equal to 10".

B: "at least one number is 5".

Which of the following option(s) is/are correct?

- Event A is a simple event.
- Events A and B are not mutually exclusive events.
- Event B is a compound event.
- Events A and B are mutually exclusive events.

**Q.**Let ‘head’ means one and ‘tial’ means two and the coefficients of the equation ax2+bx+c=0 are chosen by tossing a coin. The probability that the roots of the equation are non – real, is equal to:

- 58
- 78
- 38
- 18

**Q.**A four digit number (numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is equal to the sum of its last two digits. If a four digit number is picked up at random, then the probability that it is a lucky number is:

- 0.067
- 0.67
- None
- 0.07

**Q.**Three athletes A, B and C participate in a race. Both A and B have the same probability of winning the race and each is twice as likely to win as C. The probability that B or C wins the race is

- 23
- 35
- 34
- 1315

**Q.**If two different numbers are taken from the set {0, 1, 2, 3, ⋯, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is:

- 655
- 1255
- 1445
- 755

**Q.**There is a group of 30 students from class XIth and class XIIth.

EventX={ Students in classXIth}

EventY={ Students in classXIIth}

X and Y are mutually exclusive events.

- True
- False

**Q.**List- IList-II(I)logx+1(4x3+9x2+6x+1)+log4x+1(x2+2x+1)(P) −1=5, then the number of solution is(II)If f(x)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩(34)tan4xtan3x , 0<x<π2a+2 , x=π2(1+|cotx|)ab|tanx| , π2<x<π(Q) 0is continuous at x=π2, then a+b=(III) If I=3∫−11x2dx , then |3I|=(R) 1(IV)If x-z plane divides the line joining of the points(S) 2P(3, a, −4) and Q(2, −23, 5) in the ratio 3:1, then, a=(T) 3(U)Does notexist

Which of the following is the only CORRECT combination?

- (I)→(U)
- (II)→(P)
- (IV)→(Q)
- (IV)→(T)

**Q.**

If A and B are two mutually exclusive and exhaustive events, then P(B)=1−P(A).

True

False

**Q.**If 1+3p3, 1−p4 and 1−2p2 are probabilities of mutually exclusive events of a random experiment, then the range of p is

- [13, 12]
- [14, 12]
- [13, 23]
- [13, 25]

**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

- 1/5
- 2/3
- 3/5
- 1

**Q.**Two events A and B have the probabilities 0.25 and 0.5 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability of neither A nor B occurs is equal to:

- 0.61
- 0.39
- 0.29
- 0.19