MTH202 Quiz 4 Solution by Abu Huraira Faraz

MTH202 QUIZ NO: 4 SOLUTION FILE

EFFORT BY: ABU HURAIRA FARAZ

1. What is the probability of getting a number greater than 5 when a dice is tossed? Answer: 1/6

Q2. Suppose that A and B are events in a sample space. If A and b disjoint, could P (A) = 0.6 and P (B) = 0.5?

Answer: No

3. The ____ of the experiment is the set of possible outcomes. Answer sample space
4. An event is a subset of? Answer: sample space
5. A boy have 3 red and 4 blue balls, what is the probability that a ball chosen from the boy is blue? Answer: 3/7
6. Among 20 people, 15 either swim or jog or both. If 5 swim and 6 swim and jog. How many jog? Answer: 16.

Q7. An urn contains six red and nine blue balls. What is the probability that a ball chosen from the urn is blue?

Answer: 9/15

8. _____ is a procedure that yields a given set of possible outcomes? Answer: experiment
9. How many integers from 1 through 1002 are multiples of 4? Answer: 250.5
10. The probability of a an event lies between 0 and 1. Answer: true

Q11. When a dice and a coin are tossed together, then which of the following is the sample space?

Answer: {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

12. If two light bulbs are chosen at random from 5 bulbs of which 3 are defective, then which of the following is the probability that none is defective? Answer: 2/8
13. If A and B are finite sets then the mathematical representation of inclusion-exclusion principle.
14. A tree is normally constructed from ____. Answer: left to right
15. Let a and B be subsets of U with n (A) = 12, n (B) = 15, n (A’) = 17, and n (A intersection B) = 8, then n (U) = ____. Answer: 29
16. A boy have 5 res and 7 blue balls, what is probability that a ball chosen from the boy is red? Answer: 5/12
17. If A and B are finite set then n (AUB) = ____. Answer: n (A) +n (B) – n(𝑨 ∩ 𝑩)
18. If A and B are disjoint finite sets then n (AUB) = ____. Answer: n (A) + n (B)
19. There are 5 girls’ students and 20 boys students in a class. How many students are there in total? Answer: 25
20. If A is only set and U is the universal then N (A’) = ____. Answer: n (U) – n (U∩A)
21. If A and B are disjoint sets then the mathematical representation of inclusion-exclusion principle.Answer: n

(AUB) = n (A) + n (B)

23. If A and B are disjoint sets then P (A B) =………… Answer: P (A)
24. If B is a subset of A then P(A/B)= 1 Answer: True
25. P(AC /B)=1 - P(A/B) Answer: True
26. If A and B be events with P (A) =1/3. P (B) =1/4 and P (A intersection b)=1/6, then P(A U B) = .

Answer: 5/12

27. P (A/B) = P (A n b)/P (B), where . Answer: P (B) > 0
28. If A and B be events with P (A) =1/3. P(B)=1/4 and P(A intersection b)=1/6, then P(A/B) = Answer: 2/3
29. Conditional probability of A given B is defined as . Answer: P (A n B) / P (B)
30. If X and Y are independent random variables and a and b are constant, then Var(aX+bY) is equal to

Answer: A^2 Var(X) + b^2Var(Y)

31. If the random variable X denotes the number of heads when three distinct coins are tossed, then X assumes the value Answer: 0,1,2,3
32. Which of the followings is the probability of getting a 6 when a dice is tossed? Answer: 1/6
33. Conditional probability of B given A is defined as . Answer: P (A n B) / P (A)
34. If A is a subset of B then P(A I B) = P(A)/P(B) Answer: True
35. What is the probability of the number of one head when two fair coins are tossed? Answer: 2/4
36. If A and B are disjoint sets then P (A/B) = ? Answer: P (A)
37. Which of the followings is the product set A*B*C? where A= {a}, B={b}, and C={c,d}

Answer: {(a, b, c), (a, b, d)}

38. Among 20 people, 15 either swim or jog or both. If 5 swim and 6 swim and jog, how many jog? Answer: 16
39. Let X= {1, 2, 3}, then 2-combinations of the 3 elements of the set X are ? Answer: {1, 2}. {1, 3} and {2, 3}
40. P (A n B) = P (A). P(A/B) Answer: False
41. If B is a subset of A then P(A/B) = 1 Answer: True
42. An expected value of a random variable is equal to its mean Answer: True
43. If A and B are two independent events then P( A n b ) = Answer: P (A) P (B)