Wize High School Algebra II Textbook (Common Core) > Probability and Counting
Counting and Probability
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Counting and Probability
Combinations calculate the number of outcomes where we do not care about the order. To calculate the probability of a combination, we must take into consideration of the number of favorable outcomes over the number of possible outcomes.
Example
There are 26 cases, and 5 of them contains the word "GOLD". In order to win a million dollars, the contestant must select, without replacement, 3 cases that contains the word "GOLD". What is the probability that they will win a million dollars?
Number of favorable outcomes:
(there are 10 different ways to choose 3 of 5 "GOLD" cases)
Number of possible outcomes:
(there are 2,600 different ways to choose 3 different cases out of 26 cases)
Probability of choosing 3 "GOLD" cases:
= [Number of favorable outcomes] divided by [Number of possible outcomes]
Wize Tip
You can also solve this using Hypergeometric Probability.
Example: Counting and Probability
There are 5 male employees and 3 female employees in the marketing department. What is the probability of randomly selecting 2 of each to launch a new campaign?
You need to select 2 out of 5 male employees AND (multiplication rule) select 2 out of 3 female employees → You are selecting 4 out of 8 total employee.
Translation: there are 30 different ways of selecting 2 of each gender out of 70 different ways to select 4 of 8 employees.
Seven people are right-handed, and 3 people are left-handed. What is the probability of randomly selecting 2 of each?