#### Introduction To Probability Theory Model Question Paper

11th Standard

Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 60
10 x 1 = 10
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. 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

3. A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

(a)

${3\over 16}$

(b)

${3\over 8}$

(c)

${1\over 4}$

(d)

${5\over 8}$

4. If A and B are two events such that A⊂B and P(B)$\neq o$ ,then which of the following is correct?

(a)

$P(A/B)={P(A)\over P(B)}$

(b)

P(A/B)<P(A)

(c)

P(A/B)$\ge$P(A)

(d)

P(A/B)>P(B)

5. 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

6. If two events A and B are such that $P(\overline{A})={3\over10}$and $P(A \cap \overline{B})={1\over2},$then$P(A\cap B)$ is

(a)

${1\over2}$

(b)

${1\over3}$

(c)

${1\over4}$

(d)

${1\over5}$

7. If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation $x^2+ax+b=0$ is

(a)

${3\over 16}$

(b)

${5\over 16}$

(c)

${7\over 16}$

(d)

${11\over 16}$

8. In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

(a)

${2\over 11}$

(b)

${3\over 11}$

(c)

${5\over 11}$

(d)

${7\over 11}$

9. Ten coins are tossed. The probability of getting at least 8 heads is

(a)

$7\over 64$

(b)

$7\over 32$

(c)

$7\over 16$

(d)

$7\over 128$

10. If m is a number such that m $\le$ 5, then the probability that quadratic equation 2x2+2mx+m+1=0 has real roots is

(a)

${1\over 5}$

(b)

${2\over 5}$

(c)

${3\over 5}$

(d)

${4\over 5}$

11. 10 x 2 = 20
12. 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
$P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 }$

13. 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)=0.421, P(B)=0.527  P(C)=0.042

14. 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?

15. 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

16. If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail (ii) at most two tails

17. A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that (i) all are red (ii) one red and 2 black

18. Nine coins are tossed once, find the probability to get at least two heads

19. Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
$P(\overline { A } \cup \overline { B } )$

20. A die is tossed thrice. find the probability of getting an odd number atleast once?

21. The ratio of the number of boys to the number of girls in a class is 1:2. It is known that the probability of a girl and a boy getting a first class are 0.25 and 0.28 respectively. Find the probability that a student chosen  at random will get first class?

22. 5 x 3 = 15
23. If for two events A and B, P(A)=$\frac{3}{4}$, P(B)=$\frac{2}{5}$ and A$\cup$B=S (sample space), find the conditional probability P(A/B).

24. One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that (i) both are white (ii) both are black (iii) one white and one black.

25. The chances of A, B, and C becoming manager of a certain company are 5 : 3: 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?

26. If A and B are two events associated with a random experiment for which
P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15.
Find (i) P(only B)
(ii) P(B)
(iii) P(only A)

27. 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.

28. 3 x 5 = 15
29. Given P(A) = 0.4 and P(A$\cup$B)=0.7. Find P(B) if
(i) A and B are mutually exclusive
(ii) A and B are independent events
(iii) P(A / B) = 0.4
(iv) P(B / A) = 0.5

30. Two cards are drawn from a pack of 52 cards in succession. Find the probability that both are Jack when the first drawn card is (i) replaced (ii) not replaced.

31. 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?