Complementary Events
If there is a 35% chance of a thunderstorm tomorrow, what is the probability of it not raining, assuming no rain without thunderstorms?
65%
The probability of rolling a 1 or a 6 on a fair six-sided die is 2/6. What is the probability of rolling any other number?
4/6 or 2/3
In a group of students, 10 like pizza, 15 like burgers, and 5 like both. What is the probability that a student selected at random likes either pizza or burgers?
20/30 = 2/3
What is the probability of flipping two coins and getting either two heads or two tails?
0.5 or 1/2
If you draw two cards from a deck without replacement, what is the probability that both are aces?
4/52 x 3/51 = 1/221
The probability of selecting a red card from a deck is 1/2. If the probability of drawing a card that is not red is increased by 0.05 due to some faulty cards being discarded, what is the new probability of drawing a red card?
0.45
If the probability of drawing a king or a queen from a standard deck of cards is 8/52, what is the probability of not drawing a king or queen? Provide your answer as a fraction.
44/52 or 11/13
In a class, 8 students play football, 10 play basketball, and 4 play both. How many students play either football or basketball?
14
A bag contains 4 red marbles, 5 blue marbles, and 6 green marbles. If two marbles are drawn with replacement, what is the probability of getting a red and then a green marble?
4/15 x 6/15 = 24/225 = 8/75
You have a bag of 5 red, 4 blue, and 3 green marbles. Two marbles are drawn without replacement. What is the probability that the first marble is red and the second marble is blue?
5/12 x 4/11 = 20/132 = 5/33
In a classroom, 70% of the students wear glasses. If a student is randomly selected, what is the probability that they do not wear glasses? Express your answer as a decimal.
0.3
In a school competition, the probability of Team A winning is 0.35, the probability of Team B winning is 0.5, and the probability of Team C winning is 0.15. What is the combined probability of either Team B or C winning?
0.65
In a survey, 40 people were asked if they liked coffee or tea. 25 said coffee, 15 said tea, and 10 said both. How many people like either coffee or tea (or both)?
30
Two dice are rolled. What is the probability of rolling a 5 and a 6?
2/36 = 1/18
A box contains 4 white balls and 6 black balls. Two balls are drawn without replacement. What is the probability that both are white?
4/10 x 3/9 = 12/90 = 2/15
In a board game, the probability of landing on a green space is 0.4, and the probability of landing on a red or blue space combined is 0.5. What is the probability of not landing on any of these spaces?
0.1
You have a spinner that has 8 equally sized sections, numbered 1 to 8. What is the probability of landing on an even number, and what is the complementary probability of landing on an odd number?
P(even) = 4/8 = 1/2, P(odd) = 1/2
In a class of 50 students, 30 study English, 25 study Math, and 10 study both subjects. If a student is selected at random, what is the probability that the student studies either English or Math, but not both?
35/50 = 7/10
A jar contains 3 red, 2 blue, and 5 yellow marbles. If two marbles are drawn without replacement, what is the probability of drawing two blue marbles?
2/10 x 1/9 = 1/45
A class has 8 boys and 7 girls. If two students are selected at random without replacement, what is the probability that both are girls?
7/15 x 6/14 = 42/210 = 1/5
In a company survey, 62% of employees like their work environment, 20% dislike it, and the rest are undecided. What is the probability that an employee is undecided?
0.18
The probability of hitting a target is 0.45, and the probability of missing is 0.55. If a player takes three shots, what is the probability that they miss all three shots?
0.55 × 0.55 × 0.55 = 0.166375
In a survey of 100 people, 60 people like tea, 50 people like coffee, and 20 people like both. What is the probability that a randomly selected person likes neither tea nor coffee?
10/100 = 1/10
You roll a die twice. What is the probability of rolling an odd number on the first roll and a number greater than 4 on the second roll?
3/6 x 2/6 = 6/36 = 1/6
A box contains 4 green balls and 3 yellow balls. If two balls are drawn without replacement, what is the probability that one is green and one is yellow?
4/7 x 3/6 + 3/7 x 4/6 = 12/42 + 12/42 = 24/42 = 4/7