2nd PUC Maths Question Bank Chapter 13 Probability Ex 13.1

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Karnataka 2nd PUC Maths Question Bank Chapter 13 Probability Ex 13.1

2nd PUC Maths Probability NCERT Text Book Questions and Answers Ex 13.1

Question 1.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E∩F) =0.2, find p(E|f) and P(F|E).
Answer:

Question 2.
Compute P(A|B), if P(B) = 0.5 and P (A∩B) = 0.32
Answer:

Question 3.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4 Find.
(i) P(A∩B)
(ii) P(A|B)
(iii) P(A∪B)
Answer:

Question 4.
Evaluate P(A∪B), if 2P(A) = \(P(B)=\frac { 5 }{ 13 } { and }{ \quad P }({ A }|{ B })=\frac { 2 }{ 5 } \)
Answer:

Question 5.
\(\text { If } P(A)=\frac{6}{11}, P(B)=\frac{5}{11} \text { and } P(A \cup B)=\frac{7}{11}\) find
(i) P(A∩B)
(ii) P(A|B)
(iii) P(B|A)
Answer:

Question 6.
A coin is tossed three times, where
(i) E : head on third toss, F : heads on first two tosses
(ii) E : at least two heads, F : at most two heads
(iii) E : at most two tails, F : at least one tail
Answer:
sample space {HHH, HHT, HTT, TTT, THH, TTH, THT, HTH}


Question 7.
Two coins are tossed once, where
(i) E : tail appears on one coin, F : one coin shows head
(ii) E: no tail appears, F: no head appears
Answer:

Question 8.
A die is thrown three times,
E : 4 appears on the third toss,
F : 6 and 5 appears respectively on first two tosses
Answer:

Question 9.
Mother, father and son line up at random for a family picture
E : son on one end,
F : father in middle
Answer:
sample space [MFS, MSF, SMF, SFM, FMS, FSM]

Question 10.
A black and a red dice are rolled.
(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Answer:
(a) E : Sum gr than 9 = {(4,6), (6,4), (5,5), (6,5), (5,6), (6,6)}
F : Black resulted in 5 = {(5,1), (5,2), (5,3), (5,4),(5,5), (5,6)}
E∩F = sum gr than 9 and black die resulted in 5

Question 11.
A fair die is rolled. Consider events E = {1,3, 5}, F = (2,3} and G = {2, 3,4,5} Find
(i) P (E|F) and P (F|E)
(ii) P (E|G) and P (G|E)
(iii) P ((E∪F)|G) and P (E∩F)|G)
Answer:

Question 12.
Assume that each born child is equally likely to be a girl. If a family has two children, what is the conditional probability that both are girls given that
(i) the youngest is a girl.
(ii) at least one is girl ?
Ans:
E : Both are girls {GG, BB, GB, BG}
F: Youngest is a girl
G: At least one is girl

Question 13.
An instructor has a question bank  consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice question and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question ?
Answer:
E : Easy question
F: Multiple choice question Given 300 – E (T|F)
500 – E multiple 200 – D (T|F)
400 – D (multiple)

Question 14.
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4
Answer:
E : Sum of the number is 4 [(1,3), (3,1), (2,2)]
F : The number appearing are different E∩F different number but sum is 4 throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4′.
Answer:
E : Sum of the number is 4 [(1,3), (3,1), (2,2)]
F : The number appearing are different
E∩F : different number but sum is 4
\(P(F)=\frac{30}{36}\)
{except (1,1) , (2,2) , (3,3) ,(4,4) ,(,5,5) ,(6,6)}

Question 15.
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the 1 die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
Answer:
{(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (1,H), (1,T), (2,H), (2,T), (4,T), (4,H), (5,T), (5,H), (6,T),(6,H)}
E: coin shows a tail

∴ Event is called impossible event
In each of the Exercise 16 and 17 choose the correct answer:

Question 16.
If P(A) = \(\frac{1}{2}\),P(B) = 0, then P( A|B) is
(A) 0
(B) \(\frac{1}{2}\)
(C) not defined
(D) 1
Answer:

defined
Option “C”

Question 17.
If A and B are events such that P (A|B) = P (B|A), then
(A) A⊂B but A≠B
(B) A = B
(C) A∩B =φ
(D) P(A) = P(B)
Answer:

Option ‘D’