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Test: Probability And Expected Value By Mathematical Expectation- 2 - CA Foundation MCQ


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30 Questions MCQ Test - Test: Probability And Expected Value By Mathematical Expectation- 2

Test: Probability And Expected Value By Mathematical Expectation- 2 for CA Foundation 2024 is part of CA Foundation preparation. The Test: Probability And Expected Value By Mathematical Expectation- 2 questions and answers have been prepared according to the CA Foundation exam syllabus.The Test: Probability And Expected Value By Mathematical Expectation- 2 MCQs are made for CA Foundation 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Probability And Expected Value By Mathematical Expectation- 2 below.
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Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 1

(Direction 1 - 15) Write down the correct answers. Each question carRies 1 mark.

Q. If x and y are independent, then

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 2

If a random variable x assumes the values x1 , x2 , x3 , x4 with corresponding probabilities p1 , p2 , p3 , p4 then the expected value of x is

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Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 3

f(x), the probability mass function of a random variable x satisfies

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 4

Variance of a random variable x is given by

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 5

If two random variables x and y are related by y = 2 – 3x, then the SD of y is given by

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 6

Probability of getting a head when two unbiased coins are tossed simultaneously is

Detailed Solution for Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 6

Favourable number of outcomes, getting one head ={HT, TH}
Total number of outcomes ={HH, HT, TH, TT}
Probability =2/4=1/2

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 7

If an unbiased coin is tossed twice, the probability of obtaining at least one tail is

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 8

If an unbiased die is rolled once, the odds in favour of getting a point which is a multiple of 3 is

Detailed Solution for Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 8

Total number =6
Getting a 'multiple of 3' = 2 . So, probability = 2/6 =1/3

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 9

A bag contains 15 one rupee coins, 25 two rupee coins and 10 five rupee coins. If a coin is selected at random from the bag, then the probability of not selecting a one rupee coin is

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 10

A, B, C are three mutually independent with probabilities 0.3, 0.2 and 0.4 respectively.What is P (A ∩ B ∩ C)?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 11

If two letters are taken at random from the word HOME, what is the Probability that none of the letters would be vowels?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 12

If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Spade or an ace?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 13

If x and y are random variables having expected values as 4.5 and 2.5 respectively, then the expected value of (x–y) is

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 14

If variance of a random variable x is 23, then what is the variance of 2x+10?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 15

What is the probability of having at least one ‘six’ from 3 throws of a perfect die?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 16

(Direction 16 - 38) Write down the correct answers. Each question carries 2 marks.

Q.Two balls are drawn from a bag containing 5 white and 7 black balls at random. What is the probability that they would be of different colours? 

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 17

What is the chance of throwing at least 7 in a single cast with 2 dice?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 18

What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 19

If two unbiased dice are rolled together, what is the probability of getting no difference of points?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 20

If A, B and C are mutually exclusive independent and exhaustive events then what is the probability that they occur simultaneously?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 21

There are 10 balls numbered from 1 to 10 in a box.if one ofthem is selected at random whatisthe probability that the number printed onthe ball woukd be an odd number greater than 4

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 22

Following are the wages of 8 workers in rupees:

50, 62, 40, 70, 45, 56, 32, 45

If one of the workers is selected at random, what is the probability that his wage would be lower than the average wage?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 23

A, B and C are three mutually exclusive and exhaustive events such that P (A) = 2 P (B) = 3P(C). What is P (B)?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 24

For two events A and B, P (B) = 0.3, P (A but not B) = 0.4 and P (not A) = 0.6. The events A and B are

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 25

A bag contains 12 balls which are numbered from 1 to 12. If a ball is selected at random, what is the probability that the number of the ball will be a multiple of 5 or 6 ?

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 26

Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?

Detailed Solution for Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 26

P(A|B) = P(A&B)/P(B)
So first we have to find P(A&B)
P(AUB) = P(A) + P(B) - P(A&B)3/4 = 3/5 + 2/3 - P(A&B)
Multiply through by 60
45 = 36 + 40 - 60P(A&B)
45 = 76 - 60P(A&B)
-31 = -60P(A&B)
31/60 = P(A&B)
Go back to 
P(A|B) = P(A&B)/P(B)
P(A|B) = (31/60)/(2/3)
P(A|B) = (31/60)(3/2)
P(A|B) = 31/40 = 0.775

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 27

For two independent events A and B, what is P (A+B), given P(A) = 3/5 and P(B) = 2/3?

Detailed Solution for Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 27

P(A + B) = 13/15
Step-by-step explanation:
P(A) = Probability of Event A Heppening
P(A') = Probability of Event A not Happeining
P(A) = 3/5  => P(A') = 1 - 3/5  = 2/5
P(B) = 2/3  => P(B') = 1 - 2/3  = 1/3
P(A + B) = 1 - Probability of Event A & B not happening
P(A + B) = 1  - P(A')P(B')
=> P(A + B) = 1  -  (2/5)(1/3)
=> P(A + B) = 1  -  2/15
=> P(A + B) = 13/15

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 28

If P (A) = p and P (B) = q, then

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 29

​If P ( ∪ B ) = 5/6, P(A) = ½ and P ( ) = 2/3, , what is P (A ∪ B) ?

Detailed Solution for Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 29

P(A u B ) = P(A) + P(B) - P(A Π B )

5/6 = 1/2 + 2/3 - P ( A Π B )

5/6 - 7/6 = - P ( A Π B )

-2/6 = - P( A Π B )

P ( A Π B ) = 1/3

Test: Probability And Expected Value By Mathematical Expectation- 2 - Question 30

If for two independent events A and B, P (A ∪ B) = 2/3 and P (A) = 2/5, what is P (B)?

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