# Probability Problems

Looking for help on the following 3 questions:

Births of Twins The probability that a birth will result in twins is .012. Assuming independence (perhaps not a valid assumption), what are the probabilities that out of 100 births in a hospital, there will be the following numbers of sets of twins?

48. At most 2 sets of twins

===========================================

Management The survey discussed in Example 5 also found that customers overpay for 1 out of every 10 items, on average. Suppose a customer purchases 15 items. Find the following probabilities.

24. A customer overpays on 3 items.

==========================================

66. Cheating According to a poll conducted by U.S. News and World Report, 84% of college students believe they need to cheat to get ahead in the world today.§

a. Do the results of this poll indicate that 84% of all college students cheat? Explain.

Not 84% of the college students cheat. This cannot be said for sure since not all college students were polled.

b. If this result is accurate and 100 college students are asked if they believe that cheating is necessary to get ahead in the world, what is the probability that 90 or more of the students will answer affirmatively to the

question?

#### Solution Preview

These problems require the knowledge of the binomial distribution. In general, if the random variable X follows the binomial distribution with parameters n and p, we write X ~ Bin(n, p), where p is the probability of success on a single trial, and n is the number trials. Thus, the probability of getting exactly k successes in n trials is given by the function:

P(X = k) = (n C k) * p^k * (1-p)^(n-k)

where n C k (pronounced "n choose k") is given by n!/[k! * (n-k)!]

For more details on the binomial ...

#### Solution Summary

Solution gives a brief intro to the binomial distribution and then gives step-by-step solutions.