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#### Important questions-Introduction To Probability Theory

11th Standard

Reg.No. :
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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 50

Part A

5 x 1 = 5
1. Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

(a)

${3\over4}$

(b)

${10\over23}$

(c)

${1\over2}$

(d)

${10\over21}$

2. Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

(a)

${19\over 33}$

(b)

${17\over 33}$

(c)

${23\over 33}$

(d)

${13\over 33}$

3. A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13

4. A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies${(x-10)(x-50)\over x-30}\ge0$, then P(A) is

(a)

0.20

(b)

0.51

(c)

0.71

(d)

0.70

5. If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

(a)

${5\over 13}$

(b)

${1\over 13}$

(c)

${4\over 13}$

(d)

${7\over 13}$

6. Part B

5 x 2 = 10
7. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
$P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 }$

8. A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

9. For a sports meet, a winners’ stand comprising of three wooden blocks is in the form as shown in figure. There are six different colours available to choose from and three of the wooden blocks is to be painted such that no two of them has the same colour. Find the probability that the smallest block is to be painted in red, where red is one of the six colours.

10. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

11. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) =$\frac { 2 }{ 5 }$,  P(B)=$\frac { 3 }{ 5 }$,  P(C)=-$\frac { 1 }{ 5 }$,  P(D) =$\frac { 1 }{ 5 }$

12. Part C

5 x 3 = 15
13. A problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving $\frac { 1 }{ 3 } ,\frac { 1 }{ 4 }$ and $\frac { 1 }{ 5 }$ (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

14. Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

15. If and are mutually exclusive events P(A)=$\frac{3}{8}$ and P(B)=$\frac{1}{8}$ , then find
(i) P($\bar { A }$)
(ii) $P(A\cup B)$
(iii) $P(\bar { A } \cap B)$
(iv) $P(\bar { A } \cup \bar { B } )$

16. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) $P(A\cup B)$
(ii) $P(A\cap \bar { B } )$
(iii) $P(\bar { A } \cap B)$

17. The probability that a girl, preparing for competitive examination will get a State Government service is 0.12, the probability that she will get a Central Government job is 0.25, and the probability that she will get both is 0.07. Find the probability that (i) she will get atleast one of the two jobs (ii) she will get only one of the two jobs.

18. Part D

4 x 5 = 20
19. Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

20. An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television, 30% of the time the husband is watching the television. Find the probability that
(i) the husband is watching the television during the prime time of television
(ii) if the husband is watching the television, the wife is also watching the television

21. When a pair of fair dice is rolled, what are the probabilities of getting the sum
(i)7
(ii) 7 or 9
(iii) 7 or 12?

22. A consulting firm rents car from three agencies such that 50% from agency L, 30% from agency M and 20% from agency N. If 90% of the cars from L, 70% of cars from M and 60% of the cars from N are in good conditions
(i) what is the probability that the firm will get a car in good condition?
(ii) if a car is in good condition, what is probability that it has come from agency N?