Probability Quiz Study Guide
Probability

When there is no chance of an event occurring, the probability of
the event is zero (0). When it is certain that an event will occur,
the probability of the event is one (1).

Theoretical Probability: probability based on reasoning written as

Experimental probability: probability based on trials written as
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑜𝑢𝑡𝑐𝑜𝑚𝑒 𝑜𝑐𝑐𝑢𝑟𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
Probability model: a mathematical model that defines the probability of an event occurring
Example: A die is rolled.
Roll
1
2
3
4
5
6
Theoretical Probability
1/6
1/6
1/6
1/6
1/6
1/6
Note: The sum of all possible
outcomes is always equal to 1.
Expected value: how many times you would expect an event to happen over a given number of trials (Remember:
expected value is an estimate)
Determined by multiplying the probability of the event occurring by the number of trials
Example: How many times would you expect a die to land on a 5 if the die is rolled 300 times?
Multiply the probability of landing on a 6 by 300: 1/6 * 300 = 50 times
Probability of compound events
Independent events: the outcome of one event does not affect the outcome of the other event (with replacement)
Probability (A and B) = Probability(A) * Probability(B)
Dependent events: the outcome of one event does affect the outcome of the other event (without replacement)
Probability (A and B) = Probability(A) * Probability(B given A)
P(A or B) = P(A)+P(B) – P(A and B)
Tree diagrams: tree diagrams can be used to show all of the possible outcomes and determine the probability of
compound events
Example: Flipping three coins simultaneously
The probability of all three coins landing on heads is 1/8.
The probability of only exactly two coins landing on tails is 3/8