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 30
Three 128
Two 124
One 61
None 32
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
1 2 3 4 5
(b) Do the probabilities add up to 1? Why should they?
i. Yes, because they do not cover the entire sample space.
ii. No, because they do not cover the entire sample space.
iii. Yes, because they cover the entire sample space.
iv. No, because they cover the entire sample space.
(c) What is the sample space in this problem?
i. 0, 1, 2, 3 personality preferences in common
ii. 1, 2, 3, 4 personality preferences in common
iii. 0, 1, 2, 3, 4, 5 personality preferences in common
iv. 0, 1, 2, 3, 4 personality preferences in common

Answer 1

Answer:

a. Probability (0) = 36/375 = 0.096

Probability (1) = 61/375 = 0.162

Probability (2) = 124/375 = 0.330

Probability (3) = 128/375 = 0.341

Probability (4) = 30/375  = 0.08  

b.  iii) Yes, because they cover the entire sample space.    

c. Obviously, the sample space in this problem is iv.

iv = {0,1,2,3,4}  personality preferences in common.    

Step-by-step explanation:

In this question, we are asked to calculated the probability of preferences in common.

As we know, the general formula for probability is:

Probability = Number of favorable outcome/ Total number of favorable outcomes

Data Given:

For 0 = 36

For 1 = 61

For 2 = 124

For 3 = 128

For 4 = 128

Total = 375 Married Couples

Probability (0) = Number of favorable outcomes/ Total Number of Favorable outcomes

Probability (0) = 36/375 = 0.096

Similarly,

Probability (1) = 61/375 = 0.162

Similarly,

Probability (2) = 124/375 = 0.330

Similarly,

Probability (3) = 128/375 = 0.341

Similarly,

Probability (4) = 30/375  = 0.08

b. Total Probability can never be greater than 1 and less than 0.

So,  Probabilities of the sample  will add up to 1

iii) Yes, because they cover the entire sample space.

Total Probability = P(0) + P(1) + P(2) + P(3) + P(4) = 1

Total Probability = 0.09 + 0.16 + 0.33 + 0.34 + 0.08 = 1

c. Obviously, the sample space in this problem is iv.

iv = {0,1,2,3,4}  personality preferences in common.