The document contains a set of 32 multiple choice questions related to probability concepts. The questions cover topics such as sample space, outcomes, limits of probability, impossible and sure events, mutually exclusive and independent events, probability calculations, probability of combinations of events, probability using cards and dice, and probability of multiple events occurring. An answer key is provided at the end listing the correct response for each question.

1. MCQs
(Probability)
NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
https://nadeemstats.wordpress.com/listofbooks/

2. 1- A set of all possible outcomes of an experiment is called:
a. Sample space b. Sample point c. Permutation d. Combination
2- A particular result of an experiment is called:
a. Outcome b. Simple event c. Compound event d. None
3- The limit of probability is:
a. 0 to 1 b. 0 to 1 c. 0 to 100 d. None
4- In case of probability is zero then the event is:
a. Impossible b. Sure c. Particular d. None
5- In case of probability is one then the event is:
a. Sure b. Impossible c. Particular d. None

3. 6- In case of impossible event the probability is:
a.One b. Zero c. Fixed d. None
7- In case of sure event the probability is:
a. Fixed b. Zero c. One d. None
8- If A and B are mutually exclusive events, 𝑃 𝐴 ∪ 𝐵 is equal to:
𝑎. 𝑃 𝐴 + 𝑃 𝐵 𝑏. 𝑃 𝐴 + 𝑃 𝐵 − 𝑃 𝐴 ∩ 𝐵
𝑐. 𝑃 𝐴 × 𝑃 𝐵 𝑑. 𝑃 𝐴
9- If A and B are mutually exclusive events then is: 𝑃 𝐴 ∩ 𝐵
a. One b. Zero c. 0 to 5 d. None
10- If A and B are not mutually exclusive events, then 𝑃 𝐴 ∪ 𝐵 is equal to:
𝑎. 𝑃 𝐴 + 𝑃 𝐵 − 𝑃 𝐴 ∩ 𝐵 𝑏. 𝑃 𝐴 + 𝑃 𝐵
c.𝑃 𝐵 d. None

4. 11- If A and B are independent events then 𝑃 𝐴 ∩ 𝐵 is equal to:
𝑎. 𝑃 𝐴 × 𝑃 𝐵 b.𝑃 𝐴 c.𝑃 𝐵 d. None
12- If A and B are dependent events then 𝑃 𝐴 ∩ 𝐵 is equal to:
𝑎. 𝑃(𝐴) × 𝑃 𝐵
𝐴 𝑏. 𝑃 𝐴 + 𝑃 𝐵 c.𝑃 𝐴 d. 𝑃 𝐵
13- 𝐼𝑓 𝑃 𝐴 = 0.4 then 𝑃 𝐴′
is equal to:
a. 0.4 b. 0.6 c. 1 d. Zero
14- If 𝑃 𝐴′
= 0.6 then 𝑃 𝐴 is equal to:
a.1 b. 0.6 c. 0.4 d. Zero
15- 𝑃 𝐴 + 𝑃 𝐴′
is equal to:
a. 1 b. 0 c.𝑃 𝐴 d. 𝑃 𝐴′

5. 16- A coin is tossed twice, the probability of 2 head occur is:
a. 1/4 b. 1/2 c. 3/4 d. None
17- A die is rolled once, the probability of even number is:
a. 3/2 b. 1/2 c. 5/2 d. None
18- Probability of getting red king card is:
a. 4/52 b. 3/52 c. 2/52 d. None
19- Probability of getting diamond face card is:
a. 3/52 b. 4/52 c. 12/52 d. None
20- Two events which cannot happen together are called:
a. Mutually exclusive events b. Not mutually exclusive events
c. Independent events d. Dependent events

6. 21- Two events which can happen together are called:
a. Not mutually exclusive events b. Mutually exclusive events
c. Independent events d. Dependent events
22- If A and B are independent events and 𝑃 𝐴 = 0.7 and 𝑃 𝐵 = 0.15 then
𝑃 𝐴 ∩ 𝐵 is:
a. 0.15 b. 0.7 c. 0.105 d. 0.85
23- If the probability of second event has not changed due to occurrence of first
event, then the events are called:
a. Independent b. Dependent c. Mutually d. Not mutually
24- If the probability of second event changed due to occurrence of first event, then
the events are called:
a. Not mutually b. Independent c. Mutually d. Dependent
25- Mutually exclusive events are also known as:
a. Disjoint events b. Joint events c. Simple event d. Composite event

7. 26- Not mutually exclusive events are also known as:
a. Joint events b. Disjoint events
c. Simple event d. Composite event
27- A card is drawn at random from an ordinary card pack of 52 playing cards, find
the probability that the card is the four of spades
a. 4/52 b. 1/52 c. 13/52 d. none
28- From a group of ten boys and eight girls, two pupils are chosen are random, find
the probability that they are both girls.
a. 28/153 b. 16/152 c. 13/153 d. none
29- A card drawn from an ordinary pack of 52 playing cards, find the probability that
the card is a Red or a diamond
a. 1 b. 0.9 c. 0.5 d. none

8. 30- A bag contains 4 white balls and 3 black balls, two balls are drawn, find the
probability both are white if First ball is replaced
a. 16/52 b. 16/49 c. 16/50 d. none
31- A bag contains 4 white balls and 3 black balls, two balls are drawn, find the
probability both are white if First ball is not replaced
a. 12/42 b. 13/42 c. 15/42 d. none
32- Three children take a test. The probability that Jawwad passes is 0.8, the
probability that Hamza passes is 0.9 and the probability that Daniyal passes is
0.7. What is the probability that all three pass?
a. 1.2 b. 0.95 c. 0.504 d. none

9. 1-a 5-a 9-b 13-b 17-b 21-a 25-a 29-c
2-a 6-b 10-a 14-c 18-c 22-c 26-a 30-b
3-b 7-c 11-a 15-a 19-a 23-a 27-b 31-a
4-a 8-a 12-a 16-a 20-a 24-d 28-a 32-c
Answers