Basic Rules
What is the probability of an event that is certain to happen?
1
What diagram helps visualize overlapping probabilities?
Venn Diagram
What is the formula for conditional probability P(A|B)?
P(A and B)/ P(B)
Two events A and B are independent if P(A and B)=?
P(A) x P(B)
There's a 20% chance of rain and a 30% chance of a test. If they are independent, what's the probability it rains and there's a test?
0.06
If P(A)=0.3 and P(B)=0.4, and A and B are mutually exclusive, what is P(A or B)?
0.7
What does the center area of a Venn Diagram represent?
Intersection (P(A and B))
WHta does P(A|B) mean in words?
The probability of A given B has occured.
If A and B are independent, is P(A|B)= P(A)?
Yes
Explain why mutual exclusivity implies dependence.
If one happens, the other cannot ( so knowing one happened affects the other).
What is the complement rule?
P(A^c)=1-P(A)
In a two-way table, what do marginal totals represent?
The totals for each row/column
When does P(A|B) equal P(A)?
A and B are independent.
You flip two coins. Are the results independent?
Yes
A box has 4 red and 6 blue marbles. One is drawn, not replaced, and another is drawn. Are the events independent?
No, b/c the probability changes after the first draw.
What must the probabilities of all outcomes in a sample space add up to?
1
True or False: Two mutually exclusive events can occur at the same time.
False
P9A and B) = 0.12 and P(B) = 0.3. Find P(A|B).
0.4
True or False: Independence means the events cannot occur at the same time.
False
True or False: If P(A|B) = P(A), A and B must be mutually exclusive.
False (implies independence, not exclusivity).
What is the addition rule for any two events A and B?
P(A or B) = P(A) + P(B) - P(A and B)
How do you find P(A or B) using a two-way table?
Add all values in A and B, then subtract the overlap (intersection).
A school survey shows 70% of students play sports, and 40% of those also do community service. What's P( community service | plays sports)?
0.4
P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2. Are A and B independent?
No, b/c 0.5 x 0.4 = 0.2, which matches (so yes, they are independent).
You roll two dice. What is the probability of getting a sum of 7 or doubles?
A: P(7) = 6/36, P9doubles) = 6/36 P9both) = 1/36, so 6+6-1 = 11/36