Question

2. 205 randomly selected students from a certain community college were asked a question "Withwhom do you find it easier to make friends?” Possible responses were 'opposite sex', 'samesex''no difference'. The students were also categorized as male or female. The followingtable records the data collected.Opposite Sex Same Sex No Difference TotalFemale 582070 148Male 241340 77Total 8233110 225a) What is the probability that a randomly selected student would say that it is easier to makefriends with the same sex or male?b. What proportion of female students answered that it is easier to make friends with the samesex?c. What probability that a male student said it easier to make friends with opposite sex?

Answer 1

The sample contains 225 students, where there are 148 females and 77 males.

The probability of an event A occurring can be calculated as

`P(A)=\frac{\text{Number of times A occured}}{Number\text{ of total events}}`

QUESTION A:

Number of students that say that it will be easier to make friends with the same sex is 33.

The probability of this event is calculated as

`P(S)=(33)/(225)`

The students who will say it is easier to make friends with males are the females that make friends with the opposite sex and the males that make friends with the same sex. The sum will be

`n(M)=58+13=71`

The probability of this can be calculated by

`P(M)=(71)/(225)`

The probability of both events occurring is calculated as

`P=P(S)+P(M)-P(S\cap M)`

The intersection of S and M is simply the number of people that say same-sex and males. This number is 13, the number of males that say same sex.

The probability is calculated as

`P(S\cap M)=(13)/(225)`

Therefore, the general probability is given to be

`\begin{gathered} P=(33)/(225)+(71)/(225)-(13)/(225) \\ P=(91)/(225) \end{gathered}`

QUESTION B:

The number of females that answered that it is easier to make friends with the same sex is 20.

There are 148 females in total.

Therefore, the proportion of females that answered that it is easier to make friends with the same sex can be calculated as

`(20)/(148)=(5)/(37)`

QUESTION C:

The number of male students that said it is easier to make friends with the opposite sex is 24.

The probability is given as

`P(S_M)=(24)/(225)=(8)/(75)_{}`