Probability Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. For k = 1, 2, 3 the box B
k
 contains k red balls and (k + 1) white balls.
Let  and A box is selected at random
and a ball is drawn from it. If a red ball is drawn, then the probability
that it has come from box B
2
, is
(a)
(b)
(c)
(d)
2. If ,  and , then
Page 2


PART-I (Single Correct MCQs)
1. For k = 1, 2, 3 the box B
k
 contains k red balls and (k + 1) white balls.
Let  and A box is selected at random
and a ball is drawn from it. If a red ball is drawn, then the probability
that it has come from box B
2
, is
(a)
(b)
(c)
(d)
2. If ,  and , then
.  is equal to
(a)
(b)
(c)
(d) 1
3. A binomial variate X has mean = 6 and variance = 2 the probability that
 is
(a)
(b)
(c)
(d) none
4. Let E
c
 denote the complement of an event E. Let E, F, G be pairwise
independent events with P(G) > 0 and
P(EnFnG) = 0. Then P(E
c 
n F
c 
| G) equals
(a) P(E
c
) + P(F
c
)
(b) P(E
c
) – P(F
c
)
(c) P(E
c
) – P(F)
(d) P(E) – P(F
c
)
5. Suppose X is a random variable which takes values0, 1, 2, 3, ... and P(X
= r) = pq
r
, where 0 < p < 1, q = 1 – p and r = 0, 1, 2, ... then :
(a)
(b)
(c)
(d) All of the above
6. A bag contains n balls. It is given that the probability that among these
Page 3


PART-I (Single Correct MCQs)
1. For k = 1, 2, 3 the box B
k
 contains k red balls and (k + 1) white balls.
Let  and A box is selected at random
and a ball is drawn from it. If a red ball is drawn, then the probability
that it has come from box B
2
, is
(a)
(b)
(c)
(d)
2. If ,  and , then
.  is equal to
(a)
(b)
(c)
(d) 1
3. A binomial variate X has mean = 6 and variance = 2 the probability that
 is
(a)
(b)
(c)
(d) none
4. Let E
c
 denote the complement of an event E. Let E, F, G be pairwise
independent events with P(G) > 0 and
P(EnFnG) = 0. Then P(E
c 
n F
c 
| G) equals
(a) P(E
c
) + P(F
c
)
(b) P(E
c
) – P(F
c
)
(c) P(E
c
) – P(F)
(d) P(E) – P(F
c
)
5. Suppose X is a random variable which takes values0, 1, 2, 3, ... and P(X
= r) = pq
r
, where 0 < p < 1, q = 1 – p and r = 0, 1, 2, ... then :
(a)
(b)
(c)
(d) All of the above
6. A bag contains n balls. It is given that the probability that among these
n balls exactly r balls are white is proportional to r
2
 (0 = r = n). A ball is
drawn at random and is found to be white. Then the probability that all
the balls in the bag are white, will be:
(a)
(b)
(c)
(d)
7. In a test, an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he
makes a guess is . The probability that he copies is  and the
probability that his answer is correct given that he copied it is . The
probability that he knew the answer to the question given that he
correctly answered it, is
(a)
(b)
(c)
(d)
8. Two events E and F are independent. If P(E) = 0.3,
= 0.5, then P(E | F) – P(F | E) equals
(a)
Page 4


PART-I (Single Correct MCQs)
1. For k = 1, 2, 3 the box B
k
 contains k red balls and (k + 1) white balls.
Let  and A box is selected at random
and a ball is drawn from it. If a red ball is drawn, then the probability
that it has come from box B
2
, is
(a)
(b)
(c)
(d)
2. If ,  and , then
.  is equal to
(a)
(b)
(c)
(d) 1
3. A binomial variate X has mean = 6 and variance = 2 the probability that
 is
(a)
(b)
(c)
(d) none
4. Let E
c
 denote the complement of an event E. Let E, F, G be pairwise
independent events with P(G) > 0 and
P(EnFnG) = 0. Then P(E
c 
n F
c 
| G) equals
(a) P(E
c
) + P(F
c
)
(b) P(E
c
) – P(F
c
)
(c) P(E
c
) – P(F)
(d) P(E) – P(F
c
)
5. Suppose X is a random variable which takes values0, 1, 2, 3, ... and P(X
= r) = pq
r
, where 0 < p < 1, q = 1 – p and r = 0, 1, 2, ... then :
(a)
(b)
(c)
(d) All of the above
6. A bag contains n balls. It is given that the probability that among these
n balls exactly r balls are white is proportional to r
2
 (0 = r = n). A ball is
drawn at random and is found to be white. Then the probability that all
the balls in the bag are white, will be:
(a)
(b)
(c)
(d)
7. In a test, an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he
makes a guess is . The probability that he copies is  and the
probability that his answer is correct given that he copied it is . The
probability that he knew the answer to the question given that he
correctly answered it, is
(a)
(b)
(c)
(d)
8. Two events E and F are independent. If P(E) = 0.3,
= 0.5, then P(E | F) – P(F | E) equals
(a)
(b)
(c)
(d)
9. If A and B are two events such that  and , then 
(a)
(b)
(c)
(d)
10. Suppose X follows a binomial distribution with parameters n and p,
where 0 < p < 1, if P(X = r)/P(X = n – r) is independent of n and r, then
(a) p = 
(b) p = 
(c) p = 
(d) none of these
11. A student appears for tests I, II and III. The student is successful if he
passes either in tests I and II or tests I and IV. The probabilities of the
Page 5


PART-I (Single Correct MCQs)
1. For k = 1, 2, 3 the box B
k
 contains k red balls and (k + 1) white balls.
Let  and A box is selected at random
and a ball is drawn from it. If a red ball is drawn, then the probability
that it has come from box B
2
, is
(a)
(b)
(c)
(d)
2. If ,  and , then
.  is equal to
(a)
(b)
(c)
(d) 1
3. A binomial variate X has mean = 6 and variance = 2 the probability that
 is
(a)
(b)
(c)
(d) none
4. Let E
c
 denote the complement of an event E. Let E, F, G be pairwise
independent events with P(G) > 0 and
P(EnFnG) = 0. Then P(E
c 
n F
c 
| G) equals
(a) P(E
c
) + P(F
c
)
(b) P(E
c
) – P(F
c
)
(c) P(E
c
) – P(F)
(d) P(E) – P(F
c
)
5. Suppose X is a random variable which takes values0, 1, 2, 3, ... and P(X
= r) = pq
r
, where 0 < p < 1, q = 1 – p and r = 0, 1, 2, ... then :
(a)
(b)
(c)
(d) All of the above
6. A bag contains n balls. It is given that the probability that among these
n balls exactly r balls are white is proportional to r
2
 (0 = r = n). A ball is
drawn at random and is found to be white. Then the probability that all
the balls in the bag are white, will be:
(a)
(b)
(c)
(d)
7. In a test, an examinee either guesses or copies or knows the answer to a
multiple choice question with four choices. The probability that he
makes a guess is . The probability that he copies is  and the
probability that his answer is correct given that he copied it is . The
probability that he knew the answer to the question given that he
correctly answered it, is
(a)
(b)
(c)
(d)
8. Two events E and F are independent. If P(E) = 0.3,
= 0.5, then P(E | F) – P(F | E) equals
(a)
(b)
(c)
(d)
9. If A and B are two events such that  and , then 
(a)
(b)
(c)
(d)
10. Suppose X follows a binomial distribution with parameters n and p,
where 0 < p < 1, if P(X = r)/P(X = n – r) is independent of n and r, then
(a) p = 
(b) p = 
(c) p = 
(d) none of these
11. A student appears for tests I, II and III. The student is successful if he
passes either in tests I and II or tests I and IV. The probabilities of the
student passing in tests I, II, III are p, q and  respectively. The
probability that the student is successful is  then the relation between
p and q is given by
(a) pq + p = 1
(b) p
2
 + q = 1
(c) pq – 1 = p
(d) None of these
12. A man takes a step forward with probability 0.4 and backward with
probability 0.6. The probability that at the end of eleven steps he is one
step away from the starting point is
(a)
(b)
(c)
(d) None of these
13. If E
1
 and E
2
 are two events such that P(E
1
) = 1/4,P(E
2
/E
1
) = 1/2  and
P(E
1
/ E
2
) = 1/4, then choose the incorrect statement.
(a) E
1
 and E
2
 are independent
(b) E
1
 and E
2
 are exhaustive
(c) E
2
 is twice as likely to occur as E
1
(d) Probabilities of the events  E
1
 n E
2
 ,  E
1
 and  E
2
 are in G.P.
14. If X and Y are independent binomial variates B and ,
then P (X + Y = 3) is
(a)
(b)