Mutually Exclusive Events
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Three coins are tossed simultaneously. List the sample space for the event.
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.
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).
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
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.
If the odds in favour of an event be 33, find the probability of the occurrence of the event.
- 4766
- 1033
- 522
- None
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
(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
Find (i) P(A∪B)
(ii) P(A' ∩B')
(iii) P(A ∩B')
(iv) P(B ∩A')
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
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)
- 150
- 3255
- 3045
- 3250
X = {Student studying French is selected}
Y = {Student studying Spanish is selected}
X and Y are mutually exclusive events.
- True
- False
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