Probability questions

Question

A rugby club has three categories of membership: adult, social and junior.

The number of members in each category, classified by gender, is shown

in the table below:

Adult Social Junior

Female: 25 35 40

Male: 95 25 80

One member is chosen at random to cut the ribbon at the opening of the

new clubhouse.

(a) Find the probability that

(i) a female member is chosen,

(ii) a junior member is chosen,

(iii) a junior member is chosen, given that a female member is

chosen.

(b) V denotes the event that a female is chosen.

W denotes the event that an adult member is chosen.

X denotes the event that a junior member is chosen.

For the events V, W and X:

(i) write down two which are mutually exclusive,

(ii) find two which are neither mutually exclusive nor

independent. Justify your answer.

Answer 1

Here is some help on the first section:

First, we need to figure out how many total females there are across all categories and add together the number of those individuals. Next, we need to figure out how many people total there are across all categories and genders and those numbers together. To find the probability of a female chosen, we simply divide the number of females by the number of total individuals and simplify to find the probability of a female being chosen.

You will repeat the same process for parts ii and iii, just adding together the number of individuals from a certain category and dividing by the number of total individuals that can be chosen from.