A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected: Age < 20 Number of Customers 70 20-30 95 30-40 67 40-50 65 50-60 76 2 60 96 One customer is chosen at random for a prize giveaway. What is the probability that the customer is at least 30 but no older than 50? What is the probability that the customer is either older than 50 or younger than 30? What is the probability that the customer is at least 50?

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A: Explanation of the answer is as follows

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.