Probability

Question 1

The probability of a sample space is 1

Answer 1

All probabilities of possible outcomes must add to 1.

Question 2

Complementary Events

Answer 2

The probability of complementary events must add up to 1. If the chance of rain is 25%, then the chance of not raining is 75%

Probability A + Probability Not A = 1

Question 3

Independent Events

Answer 3

If A and B are independent events. P(A and B) = P(A)*P(B)

Question 4

Dependent Events

Answer 4

The outcome of event A affects the outcome of event B. P(A & B) = P(A) * P(B|A)

Question 5

Mutually Exclusive. Event A or Event B

Answer 5

The probability of Event A or Event B is P(A or B) = P(A) + P(B)

Question 6

Events that are not mutually exclusive

Answer 6

P(A or B) = P(A) + P(B) - P(A and B)

Question 7

Multiple Outcomes

Answer 7

If you flip a coin 4 times, what is the probability that it lands on heads exactly 2 times?

Use permutations to determine how many ways you can get heads twice. HHTT, HTHT, TTHH, THTH –> 4!/(2!2!) = 6. Each outcome has a probability of (1/2)^4 = 1/16. So the total probability is (1/16)*(6) = 3/8

Question 8

“At Least” Problems

Answer 8

If it’s At Least 2 or more, list out the scenarios, find the probability of each scenario and add them up. If it’s at least 1, use the P(at least 1) + P (none) = 1 to solve for P(at least 1).

Question 9

Using Combinations to Solve Probability Problems

Answer 9

P(event) = favorable outcomes/total outcomes

This can also be used to solve “At Least” some problems. Find the probability of each scenario by using combinations.