How would you explain to your boyfriend or girlfriend (I know ...

[appyboo]

How would you explain to your boyfriend or girlfriend (I know they are intelligent people) who have not studied probability at all the difference between mutually exclusive events and independent events? Illustrate your answer with easy to
 
  understand examples.

Question 2

The first four deviations from the mean in a sample of n = 5 reaction times were .6, .9, 1.0, and 1.5. What is the fifth deviation from the mean? Provide a sample for which these are the five deviations from the mean.
 
  What will be an ideal response?

[chereeb]

Answer to Question 1

Mutually exclusive events are events such that if one event occurs, the other event cannot occur. For example, a U.S. Senator voting in favor of a tax cut cannot also vote against it. Independent events are events such that the occurrence of one event has no effect on the probability of the other event. For example, whether or not you ate breakfast this morning is unlikely to have any effect on the probability of a U.S. Senator voting in favor of a tax cut.

Answer to Question 2

Let d denote the fifth deviation. Then .6 + .9+1.0 + 1.5 + d = 0 or 4.0 + d = 0, so d = 4.0. One sample for which these are the deviations is x1= 4.6, x2 = 4.9, x3 = 5.0, x4 = 5.5, x5 = 0. (Obtained by adding 4.0 to each deviation; adding any other number will produce a different sample with the desired property).