Addition and multiplication theorems of probability - One Line Questions
1.
A fair coin is tossed. What is the probability of getting a head or a tail? —
1
2.
If P(A) = 0.5, P(B) = 0.5, and A and B are mutually exclusive, what is P(A ∪ B)? —
1.0
3.
If P(A) = 0.3, P(B) = 0.5, and P(A ∪ B) = 0.7, what is P(A ∩ B)? —
0.2
4.
Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)? —
0.7
5.
If P(A) = 0.4, P(B) = 0.5, and P(A ∪ B) = 0.7, find P(A ∩ B). —
0.2
6.
Given P(A) = 0.4, P(B) = 0.6, and A and B are independent events, what is P(A ∩ B)? —
0.24
7.
Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.7, what is P(A ∩ B)? —
0.28
8.
If P(A) = 0.6, P(B) = 0.7, and P(A ∪ B) = 0.9, find P(A ∩ B). —
0.3
9.
If P(A) = 0.5 and P(B) = 0.5, and A and B are independent, what is P(A ∪ B)? —
0.75
10.
If P(A) = 0.6 and P(A ∩ B) = 0.3, find P(B | A). —
0.5
11.
Two events A and B are independent. If P(A) = 0.3 and P(B) = 0.5, what is P(A ∪ B)? —
0.65
12.
Let A and B be events such that P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.1. Find P(A ∪ B). —
0.6
13.
If P(A) = 0.5 and P(B) = 0.4, and P(A ∩ B) = 0.2, find P(A ∪ B). —
0.7
14.
If P(A) = 0.6, P(B) = 0.4, and P(A ∩ B) = 0.2, find P(A ∪ B). —
0.8
15.
Two independent events A and B have P(A) = 0.5 and P(B) = 0.6. What is P(A ∪ B)? —
0.8
16.
If P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3, find P(A ∪ B). —
0.9
17.
If P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.1, find P(A ∪ B). —
0.8
18.
Given P(A) = 0.7, P(B) = 0.5, and A and B are independent, find P(A ∪ B). —
0.85
19.
If P(A) = 0.5, P(B) = 0.7, and P(A ∩ B) = 0.3, what is P(A ∪ B)? —
0.8
20.
If P(A) = 0.7, P(B) = 0.8, and P(A ∩ B) = 0.6, find P(A ∪ B). —
0.9
21.
If P(A) = 0.8, P(B) = 0.7, and P(A ∩ B) = 0.6, find P(A ∪ B). —
0.9
22.
If P(A) = 0.7, P(B) = 0.2, and A and B are mutually exclusive, what is P(A ∪ B)? —
0.9
23.
If P(A) = 0.9 and P(B) = 0.8, and P(A ∩ B) = 0.75, find P(A ∪ B). —
0.95
24.
A letter is chosen at random from the word 'PROBABILITY'. What is the probability that the letter is 'B'? —
2/11
25.
What is the probability of getting a sum of 5 when two dice are rolled? —
5/36
26.
Two dice are rolled. What is the probability of getting a sum greater than 10? —
1/6
27.
What is the probability of drawing an ace or a king from a standard deck of 52 cards in a single draw? —
2/13
28.
Two cards are drawn from a standard deck of 52 cards. What is the probability that both are hearts? —
1/221
29.
Consider two events A and B. If P(A) = 1/2, P(B) = 1/3, and P(A ∩ B) = 1/6, find P(A ∪ B). —
2/3
30.
If P(A) = 2/3, P(B) = 3/4, and A and B are independent, what is P(A ∩ B)? —
1/2
31.
What is the probability of getting an odd number or a multiple of 3 when a single die is rolled? —
2/3
32.
What is the probability that a randomly selected leap year is divisible by 400? —
1/400
33.
Two dice are rolled. What is the probability of getting a sum of 7? —
1/6
34.
If P(A) = 1/3, P(B) = 1/2, and A and B are mutually exclusive, what is P(A ∪ B)? —
5/6
35.
A coin is tossed three times. What is the probability of getting at least one head? —
7/8
36.
If P(A) = 1/2, P(B) = 1/4, and A and B are independent, what is P(A ∪ B)? —
5/8
37.
Three fair coins are tossed. What is the probability of getting exactly two heads? —
3/8
38.
A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that the first is red and the second is blue? —
6/25
39.
A card is drawn from a standard deck. What is the probability that it is a spade or a face card? —
16/52
40.
In a class of 30 students, 15 like Math, 10 like Science, and 5 like both. How many students like Math or Science? —
20
41.
A bag contains 5 red balls and 3 blue balls. If two balls are drawn without replacement, what is the probability that both are red? —
5/14
42.
What is the probability of drawing a red card or a face card from a standard deck of 52 cards? —
32/52
43.
What is the probability of selecting a prime number or an even number from the integers 1 to 10? —
7/10
44.
What is the probability that a randomly chosen integer from 1 to 100 is divisible by 2 or 3? —
67/100
45.
A number is selected at random from the first 10 positive integers. What is the probability that the number is even or a multiple of 3? —
7/10
46.
The addition theorem of probability states that for any two events A and B: —
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
47.
For any two events A and B, the probability of both A and B occurring is given by: —
P(A ∩ B) = P(A) * P(B | A)
48.
If two events A and B are mutually exclusive, then P(A ∩ B) is: —
0
49.
If A and B are two events, the probability of A or B occurring is given by: —
P(A) + P(B) - P(A ∩ B)
50.
The multiplication theorem of probability for two independent events A and B states that the probability of both A and B occurring is: —
P(A) * P(B)