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 |
35 126 125 70 19 |
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 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
| 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 |
35 126 125 70 19 |
(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.)
Total number of people surveyed = 35+126+125+70+19 = 375
| X | 0 | 1 | 2 | 3 | 4 | Total |
| p(x) | 35/375 = 0.09 | 126/375 = 0.34 | 125/375 = 0.33 | 70/375 = 0.19 | 19/375 = 0.05 | 1 |
(b) Do the probabilities add up to 1? Why should they?
Yes, because they cover the entire sample space
What is the sample space in this problem?
0, 1, 2, 3, 4 personality preferences in common
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