Question

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 Three Two One None	34 121 110 68 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. (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.

What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common1, 2, 3, 4 personality preferences in common    0, 1, 2, 3, 4, 5 personality preferences in common0, 1, 2, 3, 4 personality preferences in common

Answer 1

Isabel Briggs Myers was a pioneer in the study of personality types.

The personality types are broadly defined according to four main preferences.

Similarities and Differences in a Random Sample of 375 Married Couples
Number of Similar Preferences	Number of Married Couples
All four                     Three                     Two                     One                     None	34                     121                     110                     68 42

Total number of married couples = 375

Suppose that a married couple is selected at random.

Probability, P = number of favourable outcomes / total number of outcomes.

1) * The probability that they will have 0 personality preferences in common is

P(0 personality in common) = 42/375 = 0.11

*  The probability that they will have 1 personality preferences in common is

P(1 personality in common) = 68/375 = 0.18

* The probability that they will have 2 personality preferences in common is

P(2 personality in common) = 110/375 = 0.29

* The probability that they will have 3 personality preferences in common is

P(3 personality in common) = 121/375 = 0.32

* The probability that they will have 4 personality preferences in common is

P(4 personality in common) = 34/375 = 0.09

b) Yes the probability add to 1 because they cover the entire sample space.

c) Sample space is 0, 1, 2, 3, 4 personality preferences in common.