Basic Probability
What is the probability of flipping a head on a fair coin?
1/2
Define conditional probability.
The probability of an event occurring given that another event has already occurred.
What does it mean for two events to be independent?
One event does not affect the probability of the other.
Define a compound event.
An event made up of two or more simple events.
What does the overlapping area in a Venn diagram represent?
Events that are common to both sets (A and B)
If you roll a die, what is the probability of rolling an even number?
3/6 or 1/2
P(A|B) = 0.3, and P(B) = 0.6. What is P(A and B)?
0.18
Are flipping two coins independent events?
Yes
What is P(A or B) if A and B are mutually exclusive?
P(A) + P(B)
A Venn diagram has 10 in A, 15 in B, and 5 in both. How many total?
10 + 15 – 5 = 20
Convert 1.5 feet to inches.
18 inches
True or False: P(A|B) = P(B|A) for all events.
False
P(A) = 0.5, P(B) = 0.4, P(A and B) = 0.2. Are A and B independent?
Yes, because 0.5 × 0.4 = 0.2
You roll two dice. What’s the probability of getting a sum of 7?
6/36 or 1/6
In a two-way table, how do you find the total number of outcomes?
Add all the frequencies in the table
What is the probability of selecting a red card from a standard deck?
26/52 or 1/2
In a school, 70% of students play a sport, and 40% of those who play a sport are in honors classes. What is the probability that a randomly selected student is in an honors class given they play a sport?
0.40 or 40%
If A and B are independent, what is P(A|B)?
P(A)
What is the addition rule for compound events?
P(A or B) = P(A) + P(B) – P(A and B)
How can a Venn diagram help solve conditional probability problems?
It visually shows the relationships and intersections between events.
A jar has 5 red, 3 blue, and 2 green marbles. What is the probability of choosing a blue marble?
3/10
P(A) = 0.4, P(B) = 0.5, P(A and B) = 0.2. What is P(A|B)?
0.4
Explain how you can use a two-way table to test for independence.
Check if P(A|B) = P(A) and/or P(B|A) = P(B)
P(A) = 0.5, P(B) = 0.3, P(A and B) = 0.1. What is P(A or B)?
0.7
You are given a two-way table. How do you calculate P(A|B)?
Divide the number of outcomes in A and B by the number of outcomes in B.