#1
What is the probability of rolling a prime number with a fair six-sided die?
1/6
ExplanationTwo out of six faces on a die are prime (2, 3, 5), so the probability is 1/6.
#2
If you flip a fair coin three times, what is the probability of getting exactly two heads?
3/8
ExplanationUsing binomial probability, P(2 heads) = 3C2 * (1/2)^2 * (1/2) = 3/8.
#3
In a standard deck of 52 cards, what is the probability of drawing a red card?
1/2
ExplanationHalf of the deck is red, so the probability is 26/52, simplified to 1/2.
#4
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is randomly selected, what is the probability that it is blue?
3/10
ExplanationThere are a total of 10 balls, and 3 of them are blue. Thus, the probability is 3/10.
#5
If you roll two fair six-sided dice, what is the probability that the sum of the numbers rolled is 7?
1/6
ExplanationThere are 6 ways to get a sum of 7 out of 36 possible outcomes, so the probability is 6/36, simplified to 1/6.
#6
A jar contains 10 red marbles, 6 blue marbles, and 4 green marbles. If one marble is drawn at random, what is the probability of drawing a blue or a green marble?
1/3
ExplanationThere are a total of 20 marbles, and 10 of them are blue or green. Thus, the probability is 10/20, simplified to 1/3.
#7
You draw two cards from a standard deck of 52 cards without replacement. What is the probability that both cards are aces?
1/169
ExplanationThe probability of drawing the first ace is 4/52, and the probability of drawing the second ace is 3/51. Multiplying these gives 1/169.
#8
In a group of 10 people, what is the probability that at least two people have the same birthday?
0.99
ExplanationUsing the complement rule, P(at least 2 share a birthday) = 1 - P(no shared birthday) = 1 - (364/365)^45 ≈ 0.99.
#9
If the probability of an event A occurring is 0.6, and the probability of another event B occurring is 0.4, what is the probability of both events A and B occurring?
0.24
ExplanationThe probability of both events occurring is the product of their individual probabilities: 0.6 * 0.4 = 0.24.
#10
A committee of 5 people is to be formed from a group of 10 students. What is the probability that two specific students, Alice and Bob, are both included in the committee?
1/30
ExplanationThe probability of selecting both Alice and Bob is (1/10) * (1/9) * (8/7) * (7/6) * (6/5) = 1/30.
#11
If you randomly select a four-digit PIN code where each digit can be any number from 0 to 9, what is the probability of selecting a PIN code with all digits being different?
0.72
ExplanationThere are 10 choices for each digit, and the probability of all digits being different is (10/10) * (9/10) * (8/10) * (7/10) = 0.72.
#12
A bag contains 4 red balls, 3 blue balls, and 5 green balls. If two balls are drawn at random without replacement, what is the probability that one is red and the other is blue?
7/24
ExplanationThe probability of the first being red is 4/12, and the probability of the second being blue is 3/11. Multiplying these gives 7/24.