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)
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 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 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
You roll a standard six-sided die twice. What is the probability of rolling an even number on the first roll AND a number less than 3 on the second roll?
1/6 (or roughly 16.7%)
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%)
Alex has a 40% chance of rain today. The probability she chooses a solid shirt is 3/4 and a striped shirt is 1/4. What is the probability that she either wears a solid shirt and it does NOT rain, OR wears a striped shirt and it DOES rain?
55% (or 11/20)
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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%)