Maths Book back answers and solution for Exercise questions - Mathematics : Probability: Addition Theorem of Probability: Exercise Problem Questions with Answer

Exercise 8.4

1. If *P* (*A*) = 2/3 , *P* (*B*) = 2/5 , *P* (*A* ∪ *B*) = 1/3 then find *P* (*A* Ո *B*) .

*2. A *and* B *are two events such that,* P *(*A*)* *=* *0. 42,* P *(*B*)* *=* *0.48* *, and* P *(*A *∩* B*)* *=* *0.16* *.

Find

(i) *P,*(not *A*)

(ii) *P,*(not *B*)

(iii)* P,*(*A* or *B*)

3. If *A* and *B* are two mutually exclusive events of a random experiment and *P*(not* A*)* *= 0.45,* P *(*A *U* B*)* *= 0.65, then find* P *(*B*).

4. The probability that atleast one of *A* and *B* occur is 0.6. If *A* and *B* occur simultaneously with probability 0.2, then find *P* () + *P* () .

5. The probability of happening of an event *A* is 0.5 and that of *B* is 0.3. If *A* and *B* are mutually exclusive events, then find the probability that neither *A* nor *B* happen.

6. Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.

7. From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of it being either a red king or a black queen.

8. A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

9. Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads.

10. The probability that a person will get an electrification contract is 3/5 and the probability that he will not get plumbing contract is 5/8. The probability of getting atleast one contract is 5/7. What is the probability that he will get both?

11. In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?

12. A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two consecutive heads.

13. If *A, B, C* are any three events such that probability of *B* is twice as that of probability of *A* and probability of *C* is thrice as that of probability of*A* and if *P* (*A* ∩ *B*) = 1/6. *P *(*B *∩* C*)* *= 1/4,* P *(*A *∩* C*)* *= 1/8,* P *(*A *∪* B *∪*C*)* *= 9/10,* P *(*A *∩* B *∩*C*)* *= 1/15, then find *P *(*A*),* P *(*B*)* *and* P *(*C*)* *?

14. In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.

1. 11/15

2. (i) 0.58 (ii) 0.52 (iii) 0.74

3. 0.1

4. 1.2

5. 0.2

6. 5/9

7. 1/13

8. 13/18

9. 73/280

10. 17/40

11. 1

12. 11/48, 11/24, 11/16

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