Probability of an event and basic probability rules - One Line Questions
1.
What is the probability of a sure event (an event that is certain to happen)? —
1
2.
Let S be the sample space of an experiment. What is P(S)? —
1
3.
If P(A) = 0.3 and P(B) = 0.4, and A and B are mutually exclusive events, what is P(A or B)? —
0.7
4.
If the probability of an event is 0.8, the probability of its complement is: —
0.2
5.
If P(A) = 0.6 and P(B) = 0.5, and P(A and B) = 0.2, what is P(A or B)? —
0.7
6.
If P(A) = 0.7, what is P(not A)? —
0.3
7.
If P(A) = 0.4 and P(B) = 0.3, and A and B are independent events, what is P(A and B)? —
0.12
8.
If A and B are two events such that P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.1, find P(A ∪ B). —
0.8
9.
What is the probability of an impossible event? —
0
10.
What is the probability of the complement of an event A, denoted as P(A') or P(not A)? —
1 - P(A)
11.
If P(A) = 1/2, P(B) = 1/3, and P(A ∪ B) = 3/4, find P(A ∩ B). —
1/12
12.
What is the probability of getting a sum greater than 9 when rolling two fair dice? —
10/36
13.
A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a King? —
1/13
14.
In a random experiment, the total number of possible outcomes is 25. If event E has 5 favorable outcomes, what is P(E)? —
1/5
15.
What is the probability of getting an even number in a single throw of a fair die? —
1/2
16.
In the experiment of rolling two fair dice, what is the probability of getting a sum of 7? —
6/36
17.
Two fair coins are tossed. What is the probability of getting exactly one head? —
1/2
18.
What is the probability of drawing a spade from a standard deck of 52 playing cards? —
1/4
19.
What is the probability that a randomly selected year is a leap year? (Assume 400 years cycle, with 97 leap years) —
97/400
20.
In a single throw of a fair die, what is the probability of getting a '4'? —
1/6
21.
Three fair coins are tossed. What is the probability of getting at least one head? —
7/8
22.
What is the probability of getting no heads when three fair coins are tossed? —
1/8
23.
If there are 10 red balls and 5 blue balls in a bag, what is the probability of drawing a red ball? —
10/15
24.
In the previous scenario (10 red, 5 blue), what is the probability of drawing a blue ball? —
5/15
25.
What is the probability that a number selected at random from {1, 2, 3, ..., 100} is divisible by 7? —
14/100
26.
The odds in favor of an event A are 3:2. What is the probability of event A? —
3/5
27.
A single digit number is chosen at random from the digits 0 to 9. What is the probability that the chosen number is prime? —
4/10
28.
What is the probability of drawing a face card (Jack, Queen, King) from a standard deck of 52 cards? —
All of the above
29.
In a standard deck of 52 cards, what is the probability of drawing a card that is neither a heart nor a king? —
35/52
30.
From the same bag (4 red, 6 blue, 5 green), what is the probability of drawing a ball that is NOT green? —
10/15
31.
The odds against an event A are 2:5. What is the probability of event A? —
2/7
32.
Consider the experiment of rolling two fair dice. What is the total number of possible outcomes? —
36
33.
A bag contains 4 red, 6 blue, and 5 green balls. What is the probability of drawing a blue ball? —
6/15
34.
A number is selected at random from the first 20 natural numbers. What is the probability that the number is divisible by 3 or 5? —
9/20
35.
If P(A) = 0.25 and P(A') = 0.75, what can be concluded? —
The values are consistent with probability rules.
36.
Which rule is used to calculate the probability of the union of two events? —
Addition Rule
37.
What does it mean if P(A) = 0? —
Event A is impossible.
38.
What does it mean if P(A) = 1? —
Event A is certain to occur.
39.
If an event has probability 1, it means: —
It is guaranteed to occur.
40.
If an event has 0 probability, it means: —
It is guaranteed not to occur.
41.
The sum of probabilities of all elementary events in a sample space is: —
Equal to 1
42.
If an experiment has 'n' equally likely outcomes and event A has 'm' of these outcomes, what is the probability of event A? —
m/n
43.
If A and B are independent events, then P(A|B) is equal to: —
P(A)
44.
For any two events A and B, which formula represents the probability of A or B? —
P(A or B) = P(A) + P(B) - P(A and B)
45.
If A and B are independent events, then P(A' and B') is equal to: —
P(A') * P(B')
46.
If A and B are two mutually exclusive events, what is P(A and B)? —
0
47.
Which of the following is a fundamental property of probability? —
0 <= P(A) <= 1
48.
Let E be an event. Which statement is always true? —
All of the above
49.
What is the fundamental definition of probability of an event A, denoted as P(A)? —
The ratio of the number of outcomes favorable to A to the total number of possible outcomes.
50.
Which of the following is NOT a basic rule of probability? —
For mutually exclusive events A and B, P(A or B) = P(A) + P(B).