Probability is a branch of mathematics concerned with the likelihood of an event’s occurrence. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is to occur. This concept is widely used in various fields, including statistics, finance, gambling, science, and social science.
1. A coin is tossed twice. What is the probability of getting at least one head?
a) 1/4
b) 1/2
c) 3/4
d) 1
Answer:
c) 3/4
Explanation:
- The sample space is {HH, HT, TH, TT}.
- The favorable outcomes for at least one head are {HH, HT, TH}.
- Probability = Number of favorable outcomes / Total outcomes = 3/4.
2. A bag contains 3 red balls and 2 green balls. A ball is drawn randomly. What is the probability that it is not green?
a) 1/5
b) 2/5
c) 3/5
d) 4/5
Answer:
c) 3/5
Explanation:
- Total balls = 3 red + 2 green = 5.
- The probability of not getting green = Probability of getting red = 3/5.
3. What is the probability of drawing an ace from a deck of 52 cards?
a) 1/13
b) 1/26
c) 1/52
d) 4/52
Answer:
a) 1/13
Explanation:
- Total cards = 52.
- Number of aces = 4.
- Probability = Number of aces / Total cards = 4/52 = 1/13.
4. In a lottery, there are 10 prizes and 25 blanks. What is the probability of getting a prize?
a) 10/35
b) 25/35
c) 1/3
d) 2/5
Answer:
a) 10/35
Explanation:
- Total outcomes = 10 prizes + 25 blanks = 35.
- Probability = Number of prizes / Total outcomes = 10/35.
5. Two dice are thrown simultaneously. What is the probability of getting a sum of 7?
a) 1/6
b) 5/36
c) 1/12
d) 1/18
Answer:
a) 1/6
Explanation:
- Total possible outcomes = 6 * 6 = 36 (since each die has 6 faces).
- Favorable outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
- Probability = Number of favorable outcomes / Total outcomes = 6/36 = 1/6.
6. A jar contains 4 blue, 5 green, and 11 white marbles. If a marble is randomly selected, what is the probability that it is blue?
a) 4/20
b) 4/15
c) 1/5
d) 2/9
Answer:
c) 1/5
Explanation:
- Total marbles = 4 blue + 5 green + 11 white = 20.
- Probability of drawing blue = Number of blue marbles / Total marbles = 4/20 = 1/5.
7. An event E is said to be impossible if it has a probability of:
a) 0
b) 1/2
c) 1
d) Cannot be determined
Answer:
a) 0
Explanation:
- An impossible event has a probability of 0, indicating it cannot occur.
8. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a queen or a king?
a) 1/13
b) 2/13
c) 1/26
d) 4/13
Answer:
b) 2/13
Explanation:
- Number of queens = 4, Number of kings = 4.
- Probability = (Number of queens + Number of kings) / Total cards = (4 + 4)/52 = 2/13.
9. A box contains 5 red, 4 blue, and 6 green balls. Two balls are drawn at random. What is the probability that they are of different colors?
a) 5/7
b) 10/21
c) 25/42
d) 17/21
Answer:
c) 25/42
Explanation:
- Total balls = 5 red + 4 blue + 6 green = 15.
- Probability of drawing two balls of different colors can be calculated using combination formulas.
10. If the probability of an event happening is P(E), then the probability of the event not happening is:
a) 1 – P(E)
b) P(E)
c) 1/P(E)
d) 2P(E)
Answer:
a) 1 – P(E)
Explanation:
- The probability of an event not occurring is the complement of the event occurring.
11. In a class of 30 students, 18 play football and 15 play basketball. What is the minimum number of students who play both games?
a) 3
b) 15
c) 18
d) None of these
Answer:
a) 3
Explanation:
- Maximum possible number who play only one game = Total students - (Students playing both games).
- Minimize the students playing both games = 18 (football) + 15 (basketball) - 30 (total) = 3.
12. A jar has 3 red, 7 green, and 10 blue balls. If a ball is drawn randomly, what is the probability that it is either red or green?
a) 1/2
b) 5/8
c) 2/5
d) 1/4
Answer:
b) 5/8
Explanation:
- Total balls = 3 red + 7 green + 10 blue = 20.
- Probability of drawing red or green = (Red + Green) / Total = (3 + 7)/20 = 5/8.
13. If the odds against an event are 5:3, what is the probability of the event occurring?
a) 3/8
b) 5/8
c) 3/5
d) 2/5
Answer:
a) 3/8
Explanation:
- Probability = Favorable / (Favorable + Unfavorable) = 3 / (5 + 3) = 3/8.
14. A bag contains 3 white, 4 black, and 2 green balls. One ball is drawn at random. What is the probability that the ball drawn is either white or green?
a) 3/9
b) 5/9
c) 2/9
d) 4/9
Answer:
b) 5/9
Explanation:
- Total balls = 3 white + 4 black + 2 green = 9.
- Probability of drawing white or green = (White + Green) / Total = (3 + 2)/9 = 5/9.
15. An event A occurs with a probability of 0.2. What is the probability of the complement of A?
a) 0.2
b) 0.8
c) 0.5
d) 0.3
Answer:
b) 0.8
Explanation:
- Probability of not A = 1 - Probability of A = 1 - 0.2 = 0.8.
16. A basket contains 5 apples and 6 oranges. If you pick a fruit randomly, what is the probability that it is an apple?
a) 5/11
b) 6/11
c) 1/2
d) 3/5
Answer:
a) 5/11
Explanation:
- Total fruits = 5 apples + 6 oranges = 11.
- Probability of picking an apple = Number of apples / Total fruits = 5/11.
17. A box contains 10 screws, out of which 3 are defective. If one screw is picked at random, what is the probability that it is not defective?
a) 3/10
b) 7/10
c) 1/2
d) 6/10
Answer:
b) 7/10
Explanation:
- Total screws = 10.
- Non-defective screws = 10 - 3 = 7.
- Probability = Non-defective / Total = 7/10.
18. A couple has two children. What is the probability that both are girls if it is known that at least one of them is a girl?
a) 1/4
b) 1/3
c) 1/2
d) 3/4
Answer:
b) 1/3
Explanation:
- Possible combinations: GG, GB, BG, BB.
- Given at least one is a girl, eliminate BB.
- Remaining combinations: GG, GB, BG.
- Probability of both being girls = 1/3 (GG out of GG, GB, BG).