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                      29
Three                      124
Two                      120
One                      66
None                      36   


Suppose that a married couple is selected at random.
Required:
Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common.

Answer 1

P ( All four) = 29/375=0.07733

P ( Three A^) = 124/375= 0.33067

P ( Two A^) = 120/375= 0.32

P (One A^) = 66/375= 0.176

P (None A^) = 36/375= 0.096

Explanation:

Number of Similar Preferences  Number of Married Couples

All four 29

Three 124

Two 120

One 66

None 36

Total 375

We want to determine the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common.

P ( All four) = 29/375=0.07733

P ( Three A^) = 124/375= 0.33067

P ( Two A^) = 120/375= 0.32

P (One A^) = 66/375= 0.176

P (None A^) = 36/375= 0.096

Probability is calculated by favorable outcome divided by the total outcome.

Similarly we obtained the probabilities of the couples that they will have 0, 1, 2, 3, or 4 personality preferences in common.