# Probabilities of combinations of events

Using the given probabilities of individual events, find the probabilities that the specified combinations of those events will occur:

1. If the school cafeteria serves meat loaf, there is a 70% chance that they will serve peas. If they do not serve meat loaf, there is a 30% chance that they will serve peas anyway. The students know that meat loaf will be served exactly once during the 5-day week, but they do not know which day. If tomorrow is Monday, what is the probability that

a) the cafeteria serves meat loaf?

b) the cafeteria serves meat loaf and peas?

c) the caferteria serves peas?

2. Piano Lessons

If it rains tomorrow, the probability is .8 that John will practice his piano lesson. If it does not rain tomorrow, there is only a .4 chance that John will practice. Suppose that the chance of rain tomorrow is 60%. What is the probability that John will practice his piano lesson?

#### Solution Preview

Solution to problem 1 (about meat loaf and peas):

a. It appears that we are to assume that it is just as likely that meat loaf would be served on one day (of a 5-day week) as on another day (of that 5-day week), i.e., that the probability of serving meat loaf on Monday is equal to the probability of serving meat loaf on Tuesday, which is in turn equal to the probability of serving meat loaf on Wednesday, etc.

Since meat loaf will be served on exactly one day in the 5-day week, the probability that the cafeteria serves meat loaf on Monday is 1/5 (which, in decimal form, is .2).

b. The probability that the cafeteria serves meat loaf and peas is the product of two probabilities: the probability P1 that the cafeteria serves meat loaf, and the probability P2 that the cafeteria serves peas on a day that it serves meat ...

#### Solution Summary

Using the given probabilities of certain types of individual events, the probabilities of the specified combinations of events are determined (in detail).