CBSE Class 11 Mathematics Chapter 16 Probability Multiple Choice Questions with Answers. MCQ Class 11 Mathematics Probability with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 11 Mathematics Probability MCQs with Answers to know their preparation level.
Students who are searching for NCERT MCQ Questions for Class 11 Mathematics Probability with Answers are compiled here to get good practice on all fundamentals. Know your preparation level on MCQ Questions for Class 11 Mathematics with Answers. You can also verify your answers from our provided MCQ Class 11 Mathematics Probability with Answers. So, ace up your preparation with MCQ of Chapter 16 Mathematics Objective Questions.
MCQ Class 11 Mathematics Probability with Answers - Set - 2
Question 1:
On his vacation, Rahul visits four cities (A, B, C, and D) in a random order. The probability that he visits A first and B last is
(a) 1/2
(b) 1/6
(c) 1/10
(d) 1/12
Correct Answer – (D)
Total cities are 4 i.e. A, B, C, D
Given, Rahul visit four cities, So, n(S) = 4! = 24
Now, sample space IS:
S = {ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BDAC, BDCA, BCAD, BCDA, CABD, CADB, CBDA, CDAD, CDAB,CDBA, DABC, DACB, DBCA, DBAC, DCAB, DCBA}
Let G = Rahul visits A firsta and B last
⇒ G = {ACDB, ADCB}
⇒ n(G) = 2
So, P(G) = n(G)/n(S) = 2/24 = 1/12
Question 2 :
The probability of getting 53 Sundays in a leap year is
(a) 1/7
(b) 2/7
(c) 3/7
(d) None of these
Correct Answer – (B)
In a leap year, the total number of days = 366 days.
In 366 days, there are 52 weeks and 2 days.
Now two days may be
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday
Now there are total 7 possibilities, So total outcomes = 7
In 7 possibilities, Sunday came two times.
So, favorable case = 2
Hence, the probabilities of getting 53 Sundays in a leap year = 2/7
Question 3 :
A random variable X has poison distribution with mean 2. Then, P (X > 1.5) equals
(a) 1 – 3/e²
(b) 2/e²
(c) 3/e²
(d) 0
Correct Answer – (A)
Here m = 2
Now, P(X > 1.5) = ∑r {(e-2 × 2r)/r!} {2 ≤ r ≤ ∞}
= e-2 {2²/2! + 2³/3! + 24/4! + …}
= e-2 {(1 + 2 /1! + 2²/2! + 2³/3! + …) – 1 – 2}
= e-2 (e² – 3)
= 1 – 3e-2
= 1 – 3/e²
Question 4 :
A couple has two children. The probability that both children are females if it is known that the elder child is a female is
(a) 0
(b) 1
(c) 1/2
(d) 1/3
Correct Answer – (C)
Given, a couple has two children.
Let A denotes both children are females i.e. {FF}
Now, P(A) = (1/2)×(1/2) = 1/4
and B denotes elder children is a female i.e. {FF, FM}
P(B) = 1/4 + 1/4 = 1/2
Now, P(A ∩ B) = 1/4
Now, P(Both the children are female if elder child is female)
P(A/B) = P(A ∩ B)/P(B)
⇒ P(A/B) = (1/4)/(1/2)
⇒ P(A/B) = 1/2
Question 5 :
A bag contains 5 brown and 4 white socks . A man pulls out two socks. The probability that both the socks are of the same colour is
(a) 9/20
(b) 2/9
(c) 3/20
(d) 4/9
Correct Answer – (D)
Total number of shocks = 5 + 4 = 9
Two shocks are pulled.
Now, P(Both are same color) = (5C2 + 4C2)/9C2
= {(5×4)/(2×1) + (4×3)/(2×1)}/{(9×8)/(2×1)}
= {(5×4) + (4×3)/}/{(9×8)
= (5 + 3)/(9×2)
= 8/18
= 4/9
MCQ Class 11 Mathematics Probability with Answers
Question 6 :
The probability of getting the number 6 at least once in a regular die if it can roll it 6 times?
(a) 1 – (5/6)6
(b) 1 – (1/6)6
(c) (5/6)6
(d) (1/6)6
Correct Answer – (A)
Let A is the event that 6 does not occur at all.
Now, the probability of at least one 6 occur = 1 – P(A)
= 1 – (5/6)6
Question 7 :
Let A and B are two mutually exclusive events and if P(A) = 0.5 and P(B ̅) = 0.6 then P(A∪B) is
(a) 0
(b) 1
(c) 0.6
(d) 0.9
Correct Answer – (D)
Given, A and B are two mutually exclusive events.
So, P(A ∩ B) = 0
Again given P(A) = 0.5 and P(B ̅) = 0.6
P(B) = 1 – P(B ̅) = 1 – 0.6 = 0.4
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ P(A ∪ B) = P(A) + P(B)
⇒ P(A ∪ B) = 0.5 + 0.4 = 0.9
Question 8 :
A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year
(a) e-1/2/2
(b) e--1/2/4
(c) e-1/2/8
(d) none of these
Correct Answer – (C)
This question is based on Poisson distribution.
Now, λ = np = 500×(1/1000) = 500/1000 = 1/2
Now, P(x = 2) = {e-1/2 × (1/2)²}/2! = e-1/2 /(4×2) = e-1/2/8
Question 9 :
When a coin is tossed 8 times getting a head is a success. Then the probability that at least 2 heads will occur is
(a) 247/265
(b) 73/256
(c) 247/256
(d) 27/256
Correct Answer – (C)
Let x be number a discrete random variable which denotes the number of heads obtained in n (in this question n = 8)
The general form for probability of random variable x is
P(X = x) = nCx × px × qn-x
Now, in the question, we want at least two heads
Now, p = q = 1/2
So, P(X ≥ 2) = 8C2 × (1/2)² × (1/2)8-2
⇒ P(X ≥ 2) = 8C2 × (1/2)² × (1/2)6
⇒ 1 – P(X < 2) = 8C0 × (1/2)0 × (1/2)8 + 8C1 × (1/2)1 × (1/2)8-1
⇒ 1 – P(X < 2) = (1/2)8 + 8 × (1/2)1 × (1/2)7
⇒ 1 – P(X < 2) = 1/256 + 8 × (1/2)8
⇒ 1 – P(X < 2) = 1/256 + 8/256
⇒ 1 – P(X < 2) = 9/256
⇒ P(X < 2) = 1 – 9/256
⇒ P(X < 2) = (256 – 9)/256
⇒ P(X < 2) = 247/256
Question 10 :
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
(a) 2/9
(b) 1/9
(c) 8/9
(d) 7/9
Correct Answer – (B)
One person can select one house out of 3 = 3C1 = 3
So, three persons can select one house out of three = 3×3×3 = 27
Thus, probability that all the three can apply for the same house = 3/27 = 1/9
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.1
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.2
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.3
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16 Misc
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.1
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.2
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16.3
- NCERT Solutions Class 11 Mathematics Probability with Answers : Exercise 16 Misc
- NCERT Solutions Class 11 Mathematics Textbook download
