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.
