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

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.

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.)

(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.

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 32
132
114
60
37

Explanation / Answer

a) For the first part, where we are asked to find the estimates of the probability of the matches, we need to use the empirical distribution as the estimates. If "n" be the number of observed for a specific outcome of a random variable and "N" be the total number of possible outcome, then the empirical probability is as follows: n/N.

Hence, we get that:

b) The probabilities are add upto 1. As the outcomes are exhaustive i.e., all possible events are in the set, so we can say that this will add upto 1. That is, it covered the entire sample space.

Estimates of probability 0 1 2 3 4 37/375=0.09 60/375=0.16 114/375=0.30 132/375=0.35 32/375=0.10

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