Question

1. 205 randomly selected students from a certain community collegewere asked a question “With whom do you find it easier to makefriends?” Possible responses were ‘opposite sex’, ‘same sex’, and‘no difference'. The students were also categorized as male orfemale. The following table records the data collected.Opposite Sex Same Sex No Difference TotalFemale 581663 137Male 151340 68Total 7329205103a) What is the probability that a randomly selected student would saythat it is easier to make friends with the opposite sex?b) What proportion of male students answered that it is easier tomake friends with the opposite sex?

Answer 1

For part (a), the probability that a randomly selected student would say that it is easier to make friends with the opposite sex will be equal to the total number in the opposite sex column divided by the total number of respondents.

Thus, the probability is as follows:

`P(\text{opposite sex})=(73)/(205)\approx35.61\%`

For part (b), the proportion of male students who answered that it is easier to make friends with the opposite sex is equal to the number of males under the opposite sex column divided by the total number of respondents under the opposite sex column.

Thus, the proportion is as follows:

`P(\text{male}|\text{opposite sex})=(15)/(73)`