Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
Cumulative Standards Review

Exercise 13 Page 899

The sum of the probability of an event and the probability of its complement is Recall the formula for the number of possible combinations formed by groups of elements taken from a set of elements.

Practice makes perfect
We are told that two customers will be randomly selected to win a gift certificate at a clothing store and we want to know the probability that we do not both win. If we call the event of us both winning then we want to know
These two probabilities are complements. The sum of the probability of an event and the probability of its complement is
To find the value of we will calculate and substitute it into the above equation. We can use the theoretical probability to find
In this case, the number of possible outcomes is the number of possible unique pairs of winning customers. Notice that the order of selection is not important because we only care about which customers are selected. This means that we can use the formula for the number of combinations formed by groups of elements from a set of elements.
We are told that there are other customers in the store with us — making the total number of customers, and the value of equal Out of them, customers will be selected to win the gift certificates, so equals
Evaluate right-hand side

Write as a product

The is Now, we need to find the number of There is only one favorable outcome, the one in which we are both the winners of the gift certificates, so the is
Finally, we can find the probability of the complement of using the value of
Solve for
The probability that we will not both win the gift certificate is