Assignments Class 11 Mathematics Probability

Assignments for Class 11

Question. A party of 23 persons take their seats at a round table. The odds against two persons sitting together are:
(a) 10 : 1
(b) 1 : 11
(c) 9 : 10
(d) None of these   

Answer

A

Question. In a horse race the odds in favour of three horses are 1:2, 1:3 and 1:4. The probability that one of the horse will win the race is:
(a) 37/60
(b) 47/60
(c) 1/4
(d) 3/4     

Answer

B

Question. If a dice is thrown twice, then the probability of getting 1 in the first throw only is:
(a) 1/36
(b) 3/36
(c) 5/36
(d) 1/6   

Answer

C

Question. A coin is tossed and a dice is rolle(d) The probability that the coin shows the head and the dice shows 6 is:
(a) 1/8
(b) 1/12
(c) 1/2
(d) 1   

Answer

B

Question. The probability of happening at least one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then P(A) + P(B) = ?
(a)0.4
(b)0.8
(c)1.2
(d)1.4   

Answer

C

Question. If A and B are two independent events such that P(A) = 0. 40, P(B) = 0. 50. Find P (neither A nor B)
(a)0.90
(b)0.10
(c)0.2
(d)0.3 

Answer

D

Question. Let A and B be two events such that P(A) = 0.3 and P(A∪ B) = 0.8. If A and B are independent events, then P(B) = ?
(a) 5/6
(b) 5/7
(c) 3/5
(d) 2/5 

Answer

B

Question. The two events A and B have probabilities 0.25 and 0.50 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) 0.904
(d) None of these 

Answer

A

Question. Three athlete A, B and C participate in a race competetion.
The probability of winning A and B is twice of winning (c)
Then the probability that the race win by A or B, is:
(a) 3/2
(b) 2/1
(c) 5/4
(d) 3/1       

Answer

C

Question. An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is:
(a) 5/1296
(b) 5/1944
(c) 5 /2592
(d) None of these     

Answer

C

Question. A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is:
(a) 3/8
(b) 5/8
(c) 6/8      
(d) 10/20   

Answer

B

Question. A card is chosen randomly from a pack of playing cards.
The probability that it is a black king or queen of heart or jack is:
(a) 1/52
(b) 6/52
(c) 7/52
(d) None of these   

Answer

C

Question. If A and B are events such that P(A∪ B) = 3/ 4, P(A∩ B) = 1/ 4, P(A) = 2 / 3, then P(A∩ B) is:
(a) 5/12
(b) 3/8
(c) 5/8
(d) 1/4   

Answer

A

Question. The probability that A speaks truth is 4/5 while this probability for B is 3/4 The probability that they contradict each other when asked to speak on a fact is
(a) 4/5
(b) 1/5
(c) 7/20
(d) 3/20   

Answer

C

Question. 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 III. The probabilities of the student passing in tests I, II,III are p, q and 1/2 respectively. If the probability that the student is successful is 1/2 then
(a) p = 1, q = 0
(b) P = 2/3 , q = 1/2
(c) There are infinitely many values of p and q
(d) All of the above 

Answer

C

Question. The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of happening neither A nor B is:
(a) 0.6
(b) 0.2
(c) 0.21
(d) None of these     

Answer

B

Question. If A and B are two events such that P a ≠ 0 and P b ≠ 1, then P(A̅/B) = ? 

Answer

C

Question. If A and B are two events such that P(A∪ B) = P(A∩B), then the true relation is
(a) P(A) + P(B) = 0
(b) P(A) + P(B) =  P(A) P(B/A)
(c) P(A) + P(B) =  2P(A) P(B/A)
(d) None of these     

Answer

C

Question. Let E and F be two independent events. The probability that both E and F happens is 1/12 and the probability that neither E nor F happens is 1/2 then
(a) P(E) = 1/3 P(F) = 1/4
(b) P(E) = 1/2 P(F) = 1/6
(c) P(E) = 1/6 P(F) = 1/2
(d) None of these   

Answer

A

Question. A bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be re(d) The probability that it was drawn from B is
(a) 5/14
(b) 5/16
(c) 5/18
(d) 25/52   

Answer

D

Question. A random variable X has the probability distribution:

For the events E = {X is a prime number} and F ={X < 4}, the probability P(E ∪F) is
(a) 0.50
(b) 0.77
(c) 0.35
(d) 0.87   

Answer

B

Question. 8 coins are tossed simultaneously. The probability of getting at least 6 heads is
(a) 57/64
(b) 229/256
(c) 7/64
(d) 37/256   

Answer

D

Question. If M and N are any two events, then the probability that exactly one of them occurs is:
(a) P(M) + P(N) − 2P(M ∩ N)
(b) P(M) + P(N) − P(M ∪ N)
(c) P(M) + P(N) − 2P(M ∩ N)
(d) P(M ∩ N) − P(M ∩ N)      

Answer

A,C

Question. For two given events A and B, P(A∩B) is:
(a) not less than P(A) + P(B) −1
(b) not greater than P(A) + P(B)
(c) equal to P(A) + P(B) − P(A∪ B)
(d) equal to P(A) + P(B) + P(A∪ B)         

Answer

A,B,C

Question. If E and F are independent events such that 0 < P(E) < 1 and 0 < P(F) < 1, then:
(a) E and F are mutual exclusive
(b) E and c F (the complement of the event F) are independent
(c) Ec and c F are independent
(d) (PE/F) + P(Ec/F) = 1           

Answer

B,C,D

Question. For any two events A and B in a sample space?
(a) P(A/B)≥ P(A) + P(B)−1 /P(B) . P(B)≠0 is always true
(b) P(A∩B̅) = P(A) − P(A∩B) does not hold
(c) P(A∪B) = 1− P(A̅)P(B̅), if A and B are independent
(d) P(A∪B) = 1− P(A̅)P(B̅), if A and B are disjoint   

Answer

A,C

Question. Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happen is ½. Then:
(a) P(E) = 1/ 3, P(F) = 1/ 4
(b) P(E) = 1/ 2, P(F) = 1/ 6
(c) P(E) = 1/ 6, P(F) = 1/ 2
(d) P(E) = 1/ 4, P(F) = 1/ 3   

Answer

A,D

Question. If E and F are the complementary events of E and F respectively and if 0 < P (F) <1, then:
(a) P(E / F) + P(E̅ / F) = 1
(b) P(E / F) + P(E / F̅) = 1
(c) P(E̅ / F) + P(E / F̅) = 1
(d) P(E / F̅) + P(E̅ / F̅) = 1     

Answer

A,D

Assertion and Reason
Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Let 1 2 , ,…, n H H H be mutually exclusive events with P(Hi) > 0 ,i = 1, 2,…, n. Let E be any other event with 0 < P(E) < 1.
Assertion: (P/Hi/E) >P(E/Hi) . P(Hi) for i = 1, 2,…, n

Answer

D

Question. Consider the system of equations ax + by = 0, cx + dy = 0. 
where a,b,c,d ∈{0,1}.
Assertion: The probability that the system of equations has a unique solution, is 3/8.
Reason: The probability that the system of equations has a solution, is 1.   

Answer

B

Question. Assertion: If A and B be two events in a sample space such that P(A) = 0.3, P(B) = 0.3, then P(A∩B̅) cannot be foun(d)
Reason: P(A∩B̅) = P(A) − P(A∩ B)   

Answer

A

Question. Assertion: If P(A/ B) ≥ P(A), then P(B / A) ≥ P(B).
Reason: P(A/ B) = P(A∩B̅) / P(B).   

Answer

B

Question. Assertion: If the probability of an event A is 0.4 and that of B is 0.3, then the probability of neither A nor B occurring depends upon the fact that A and B, are mutually exclusive or not.
Reason: Two events are mutually exclusive, if they do not occur simultaneously.   

Answer

B

Paragraph–I 
Read the following passage and answer the questions. There are n urns each containing (n +1) balls such that the ith urn contains ‘i’ white balls and (n +1− i) red balls. Let 1 u be the event of selecting ith urn, i = 1, 2,3,…, n and W denotes the event of getting a white balls.

Question. If P(ui) ∝ i where i = 1, 2,3,…,n, then lim→∞ P(W) is equal to 
(a) 1
(b) 2/3
(c) 1/4
(d) 3/4   

Answer

B

Question. If n is even and E denotes the event of choosing even numbered urn (P(ui) = 1/n) then the value of P(W/E) is
(a) n+2/2n+1
(b) n+2/2(n+1)
(c) n/n+1
(d) 1/n+1   

Answer

B

Question. If P(ui) = c where c is a constant, then P(un/ W) is equal to
(a) 2/n +1
(b) 1/n +1
(c) n/n+1
(d) 1/2     

Answer

A

Paragraph– II

A fair die is tossed repeatedly until a six is obtaine(d) Let X denote the number of tosses require(d)

Question. The probability that X = 3 equals:
(a) 25/216
(b) 25/36
(c) 5/36
(d) 125/216   

Answer

A

Question. The probability that X ≥ 3 equals:
(a) 125/216
(b) 25/36
(c) 5/36
(d) 25/216   

Answer

B

Question. The conditional probability that X ≥ 6 given X > 3 equals :
(a) 125/216
(b) 25/216
(c) 5/36
(d) 25/36 

Answer

D

Paragraph– III

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls and U2 contains only 1 white ball. A fair coin is tosse(d) If head appears then 1 ball is drawn at random from U1
and put into U2. However, if tail appears then 2 balls an drawn at random from U1 and put into U2. Now, 1 ball is drawn at random from U2.

Question. The probability of the drawn ball from U2 being white is:
(a) 13/30
(b) 23/30
(c) 19/30
(d) 11/30   

Answer

B

Question. Given that the drawn ball from U2 is white, the probability that head appeared on the coin is :
(a)17/23
(b) 11/23
(c) 15/23
(d) 12/23     

Answer

D

Paragraph– IV
Box I contains three cards bearing numbers 1,2,3, ; box II contains five cards bearing numbers 1,2,3,4,5; and box III contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card
is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box i = 1, 2, 3.

Question. The probability that x1 + x2 + x3 is odd, is:
(a) 29/105
(b) 53/105
(c) 57/105
(d) 1/2     

Answer

B

Question. The probability that x1 , x2 , x3 , x1 , x2 , x3 are in an arithmetic progression, is:
(a) 9/105
(b) 10/105
(c) 11/105
(d) 7/105     

Answer

C

Match the Column

Question. Observe the following columns:

(a) A→2,3; B→1,5; C→4,5
(b) A→2,3; B→2,4; C→5,4
(c) A→2,1; B→3,2; C→5,4
(d) A→1,2; B→5,5, C→4,1   

Answer

A

Question. Observe the following columns: 

(a) A→1,2,4; B→1,3; C→1,5
(b)A→1,5,4;B→2,3; C→1,3
(c) A→4,2,1; B→3,1; C→1,5
(d) A→1,2,4;B→1,3;C→5,1     

Answer

A

Question. An electric component manufactured by ‘RASU electronics’ is tested for its defectiveness by a sophisticated testing device. Let A denote the event “the device is defective” and B the event “the testing device reveals the component to be defective”. Suppose P(A) =α and P(B/ A) = P(B′/ A′) =1−α, where 0 <α <1. If the probability that the component is not defective, given that the testing device reveals it to be defective, is λ, then the value of 2008 λ must be:         

Answer

1004

Question. Cards are drawn one by one at random form well-shuffled full pack of 52 playing cards until two aces are obtained for the first time. If N is the number of cards required to be drawn then P(N=n) = (n–1)(λ–n)(μ–n) /α x β x λ x δ where 2≤ n≤50, then the value α + β + γ + δ + 2λ + 3μ must be:           

Answer

386

Question. A special dice is so constructed that the probabilities of throwing 1, 2,3, 4,5, and 6 are 1-k/6 , 1+2k/6 , 1–k/6 , 1+k/6 , 1–2k/6 and 1+k/6 respectively. If two such dice are thrown and the probability of getting a sum equal to 9 lies between 1/9 and 2/9 ,Then the number of integral solutions of k is:     

Answer

1

Question. If X and Y are independent binomial variates B(5 ,1/2) and B(7 ,1/2) If the value of P(X +Y = 3) is λ , then the value of 40096λ must be:         

Answer

220

Question. An artillery target may be either at point I with probability 8/9 or at point II with probability 1/9. We have 21 shells each of which can be fired either at point I or II. Each shell may hit the target independently of the other shell whit probability 1/2.If the number of shells must be fired at point I to hit the target with maximum probability is x, then the value of 12x, must be:       

Answer

144