Vocab
What term describes the set of all outcomes in a sample space that are not included in an event?
Complement
If events A and B are mutually exclusive, what is the probability of both events A and B happening together?
0
What formula is used to calculate the probability of two independent events A and B both happening?
P(A) times P(B)
If a marble is chosen at random from a jar and not replaced before choosing a second marble, are the two draws independent or dependent events?
Dependent events (or not independent)
A video game screen measures 34 cm by 20 cm (total area 680 sq cm). A starship consists of two overlapping circles of radius 6 cm (area roughly 113.1 sq cm each) with an overlapping area of 20 sq cm. What is the total area occupied by the starship on the screen?
206.2 sq cm (calculated as 113.1 + 113.1 - 20)
What type of events cannot happen at the same time, meaning they share no common outcomes?
Mutually exclusive events
You roll a standard six-sided die once. What is the probability of rolling an even number or rolling a 3 or 5?
5/6
If the probability of an event occurring is 2/5, what is the probability of its complement occurring?
3/5
A school club sells 20 raffle tickets for two prizes: a laptop and a gift card. Elena bought 4 of the tickets. The principal randomly draws the winning ticket for the laptop, sets it aside, and then randomly draws the winning ticket for the gift card. What is the probability that Elena wins both prizes?
12/380 (or 3/95 / roughly 3.2%)
A shopper at an online boutique has a 0.4 (or 40%) probability of receiving a discount code with any given purchase, and each purchase is independent. The probability that they receive a discount code on two consecutive purchases is ________. The probability that they receive a discount code on the first purchase and do NOT receive one on the second purchase is ________. The probability that they do not receive a discount code on either purchase is ________.
0.16 (or 16%, calculated as 0.4 times 0.4)
0.24 (or 24%, calculated as 0.4 times 0.6)
0.36 (or 36%, calculated as 0.6 times 0.6)
What type of events are occurring when the result of the first event does not affect the probability of the second event?
Independent events
A box contains 100 balls, with 30 purple and 10 orange. What is the probability of picking a ball that is purple or orange?
40/100 (or 2/5 / 40%)
If you roll a standard six-sided die and flip a coin, what is the probability of rolling a 4 and getting heads?
1/12
A baker puts 12 freshly baked cookies into a jar: 5 are chocolate chip and 7 are oatmeal raisin. Without looking, a customer selects one cookie, eats it, and then selects a second cookie. What is the probability that the customer picks a chocolate chip cookie first and an oatmeal raisin cookie second?
35/132 (or roughly 26.5%)
Maya is running late for school and reaches into her dark closet without looking to grab a t-shirt. Her drawer contains 20 t-shirts in total, including 4 red shirts with a graphic logo, 6 blue shirts with a graphic logo, 7 plain red shirts, and 3 plain blue shirts. What is the probability that Maya pulls out a t-shirt that is red OR has a graphic logo?
17/20 (or 0.85 / 85%)
What is the term for an outcome that is being tested or observed, which isn't necessarily a desirable result?
Favorable outcome
When two events A and B overlap, what must you subtract from P(A) + P(B) to find P(A or B) so you don't count the overlapping region twice?
Answer: P(A and B)
You roll a standard six-sided die twice. What is the probability of rolling an odd number on the first roll and a number greater than 3 on the second roll?
1/4 (or 25%)
Luka is getting dressed in the dark and has 10 loose socks in his drawer: 6 are black and 4 are navy. He pulls out one sock, keeps it in his hand, and then pulls out a second sock. What is the probability that he pulls out two black socks in a row?
30/90 (or 1/3 / roughly 33.3%)
A player at an arcade has a 0.2 (or 20%) probability of winning a prize on a game on any given try, and each attempt is independent. The probability that they win prizes on two consecutive tries is ________. The probability that they win on the first try and do NOT win on the second try is ________. The probability that they lose both tries is ________.
0.04 (or 4%, calculated as 0.2 times 0.2)
0.16 (or 16%, calculated as 0.2 times 0.8)
0.64 (or 64%, calculated as 0.8 times 0.8)
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A bag contains 40 marbles. Eight are green and two are blue. What is the probability that a randomly selected marble is not green and not blue?
30/40 (or 3/4 / 75%)
You spin a spinner with equal sections of Blue and Orange twice. The probability of landing on Blue each spin is 1/3 and Orange is 2/3. What is the probability of getting the same color both times?
5/9 (calculated as 1/9 for Blue-Blue + 4/9 for Orange-Orange)
A bag contains 4 red marbles and 2 green marbles. You draw a green marble first. Is the probability that the second marble is red higher if you replace the first marble or if you do NOT replace it?
If you do NOT replace it (Without replacement: 4/5 or 80%; With replacement: 4/6 or 66.7%)
A local animal shelter is hosting an adoption weekend with 30 rescued pets, including 8 dogs that are fully vaccinated, 4 cats that are fully vaccinated, 10 dogs that still need vaccinations, and 8 cats that still need vaccinations. If a visitor randomly selects one pet to meet in the play area, what is the probability that the pet is a dog OR is fully vaccinated?
22/30 (or 11/15 / ~73.3%)