Question

1) A survey of 1250 employed people showed that 872 participated in a group health insurance plan where they worked. On the basis of this survey, what is the probability that an employed person participates in a group health insurance plan through work? Which approach to probability did you use?

2) A professor of a business statistics class takes a poll of his 120 students and finds that 81 are also taking economics, 84 are also taking accounting, and 66 are taking both economics and accounting. Based on this, what is the probability that a randomly selected student is not taking either economics or accounting?
3) A new self-serve soda machine is being installed at a local movie theatre. It asks consumers to choose one of 6 different types of soda, one of 5 different flavours that can be mixed, and one of 2 sugar options (regular or diet). How many different types of soda can be created with this machine?
4) How many different four-letter "words" can be made from the letters of the word DEMOGRAPHICS?

Answer 1

1) The probability that an employed person participates in a group health insurance plan is 0.6976. 2) The probability that a randomly selected student is not taking economics or accounting is 0.825. 3) The number of different types of soda that can be created with the self-serve soda machine is 60. 4) The number of different four-letter words that can be made from the letters of the word DEMOGRAPHICS is 11,880.

Step-by-step explanation:

1) Probability of participating in a group health insurance plan:

The probability can be calculated by dividing the number of people who participated in the plan (872) by the total number of employed people surveyed (1250):

Probability = Number of people participated / Total number of employed people surveyed = 872 / 1250 = 0.6976

We used the classical approach to probability, which assumes that all outcomes are equally likely.

2) Probability of not taking economics or accounting:

To find this probability, we need to subtract the number of people taking both economics and accounting (66) from the total number of people taking either economics or accounting (81 + 84 = 165):

Probability = (Total number taking economics or accounting - Number taking both) / Total number = (165 - 66) / 120 = 0.825

We used the classical approach to probability.

3) Number of different types of soda:

The number of different types of soda can be calculated by multiplying the number of choices for each category:

Total number of types of soda = Number of choices for soda * Number of choices for flavor * Number of choices for sugar = 6 * 5 * 2 = 60

4) Number of different words:

The number of different four-letter words can be calculated using permutations, as we are arranging the letters of the word DEMOGRAPHICS:

Total number of different words = P(12, 4) = 12! / (12-4)! = 12 * 11 * 10 * 9 = 11,880