Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Number of Similar Preferences----Number of Married Couples

All four---------------------------------31

Three----------------------------------120

Two------------------------------------120

One-------------------------------------62

None------------------------------------42

Suppose that a married couple is selected at random.

(a)Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.)

0=

1=

2=

3=

4=

(b)Do the probabilities add up to 1? Why should they?

Yes, because they do not cover the entire sample space.

No, because they do not cover the entire sample space.

Yes, because they cover the entire sample space.

No, because they cover the entire sample space.

(c) What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common

1, 2, 3, 4 personality preferences in common

0, 1, 2, 3, 4, 5 personality preferences in common

0, 1, 2, 3, 4 personality preferences in common