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Question Bank No: 3

1. A and b are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is atmost 0.3. The probability then B is selected is atmost

a)		0.6
b)		0.7
c)		0.8
d)		0.9

2. If A and B are 2 independent events such that P(A)> 0 and P(B) $\neq 1, then P (\frac{\bar{A}}{\bar{B}}) = a)$

a)		$1 - P (\frac{A}{B})$
b)		$1 - P (\frac{A}{\bar{B}})$
c)		$\frac{1 - P (A ⋃ B)}{P (B)}$
d)		$\frac{P (\bar{A})}{P (B)}$

3. A determinant is chosen at random from the set of all determinants of order 2 with elements 1 and 0 only. The probability that the value of the determinant is positive is

a)		$\frac{1}{8}$
b)		$\frac{3}{16}$
c)		$\frac{5}{16}$
d)		$\frac{1}{16}$

4. An anti-aircraft gun can take a maximum of 4 shots at an enemy plance moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2, 0.1 respectively. The probability that the gun hits the plane is

a)		0.6972
b)		0.6875
c)		0.64
d)		0.6976

5. For a biased die the probabilities of different faces to turn up are given below
pro14 The die is tossed and you are told that either face 1 or face 2 has turned up. The probability that it is face 1 is

a)		$\frac{5}{21}$
b)		$\frac{4}{17}$
c)		$\frac{3}{13}$
d)		none of these

6. The probability of an event A occuring is 0.5 and B occuring is 0.3. If A and B are mutually exclusive, then the probability of neither A nor b occuring is

a)		0.6
b)		0.5
c)		0.7
d)		none

7. The probability that an event A happens in one tral of an experiment is 0.4. If 3 independent trials are performed, the probability that A happens atleast once is

a)		0.936
b)		0.784
c)		0.904
d)		none

8. Two events A and b have probabilitities 0.25 and 0.5 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor b occurs is

a)		0.39
b)		0.25
c)		0.11
d)		none

9. Two fair dice are rolled. Let X be the event that the first die shows an even number and Y be the event that the second die shows an odd number. Then X and Y are

a)		mutually exclusive
b)		independent and nutually exclusive
c)		dependent
d)		none

10. Six boys and 6 girls sit in a row randomly. The probability that the six girls sit together or the boys and girls sit alternately is

a)		$\frac{3}{308}$
b)		$\frac{1}{100}$
c)		$\frac{2}{205}$
d)		$\frac{4}{407}$

11. A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box another ball is drawn at random and kept beside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn from the boxs are in the sequence 2 black, 4 white and 3 red is

a)		$\frac{1}{126}$
b)		$\frac{1}{630}$
c)		$\frac{1}{1260}$
d)		$\frac{1}{2520}$

12. There are two groups of subjects, one of which consists of 5 science subjects and 3 engineerign subjects and the other consits of 3 science and 5 engineering subjects. An unbaised die is cast. If number 3 or 5 turns up, a subject from group I is selected, otherwise a subject is selected from group II. The probability that an engineering subject is selected ultimately is

a)		$\frac{7}{13}$
b)		$\frac{9}{17}$
c)		$\frac{13}{24}$
d)		$\frac{11}{20}$

13. A bag contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is

a)		$\frac{25}{52}$
b)		$\frac{13}{27}$
c)		$\frac{8}{17}$
d)		$\frac{25}{51}$

14. A speaks truth in 75% of cases and B in 80% of cases. The percentage of cases they are likely to contradict each other in stating the same fact is

a)		30%
b)		35%
c)		40%
d)		25%

15. There are two bags, one of which contain 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A die is cast. If the face 1 or 3 turns up a ball is taken out from the first bag and if any other face turns up, a ball is taken from the second bag. The probability of choosing a black ball is

a)		$\frac{7}{15}$
b)		$\frac{8}{15}$
c)		$\frac{10}{21}$
d)		$\frac{11}{21}$

16. Suppose A and B are two equally strong table tennis players. Let E be the event that A beats B in 3 games out of 4 and F the event that A beats B in 5 out of 8 games. Then $\frac{P (E)}{P (F)} =$

a)		$\frac{7}{6}$
b)		$\frac{6}{7}$
c)		$\frac{8}{7}$
d)		$\frac{7}{8}$

17. A bag A conatins 3 white and 2 black balls and another bag B contains 2 white and 4 black balls. A bag and a ball out of it are picked at random. The propability that the ball is white is

a)		$\frac{2}{7}$
b)		$\frac{7}{9}$
c)		$\frac{4}{15}$
d)		$\frac{7}{15}$

18. A coin is tossed n times. The chance that the head will present itself an odd number of times is

a)		$\frac{m + 1}{2 m + 1}$ if n=2m+1
b)		$\frac{m}{2 m + 1}$ if n=2m+1
c)		$\frac{1}{2}$ only if n=2m
d)		$\frac{1}{2}$ for any n