Question

Number of Similar Preferences Number of Married couples Example 6: 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? A sample was collected and the results are shown in the table at the right. A four Threr TVO One None 131 124 71 15 a) Use the data to estimate the probability that they will have All Four preferences in common b) Find the probability of having two preferences in common. c) Find P(at least 2) d) Find P(less than 2)

Answer 1

Total no. of married couples from given data=34+131+124+71+15=375

a)

No. of couples who have all 4 preferences= 34

Pr( 4 preferences)=34/375=0.0906

b)

No of couple who 2 preferences=124

Pr(2 preferences) =124/375=0.3306

c)

Pr(atleast 2)= pr(2)+pr(3)+pr(4)

No of people having 2,3,4 preferences are =124+131+34=289

Therefore pr(atleast 2)= 289/375=0.7706

d)

Pr(less than 2)=1-pr(atleast 2)

Therefore pr(less than 2)=1-0.7707=0.2293

3. a)

No of times sum less than 4 is (1,1) (2,1) (1,2) = 3

No of times sum greater than 10 is (5,6) (6,5) (6,6) = 3

Total no of cases = 36

P( sum less than 4 or greater than 10) is = (3+3)/36 = 6/36 = 1/6.

b)

No of times doubles sum greater than 10 is (6,6) = 1

P( doubled sum greater than 10 is ) = 1/36.