Find the probability that Tom is given a task.

Question

Assume that there are 11 board members: 9 females, and 2 males including Tom. There are 5 tasks to be assigned randomly, including that of advertising meetings to the public.

(1) Find the probability that Tom is given a task.

(2) Find the probability that Tom is given the task of advertising meetings to the public.

Answer 1

Let’s walk through it step by.

(1) What’s the probability that Tom is given any task?

There are 11 total board members.

5 tasks are assigned randomly.

We want the probability that Tom is chosen for one of those tasks.

Total ways to choose 5 people from 11:

C(11, 5) = 462

Favorable outcomes (Tom is included):

Fix Tom, then choose 4 more from the remaining 10 →

C(10, 4) = 210

So:

P(Tom gets a task) = 210 ÷ 462 = 35 ÷ 77 ≈ 0.4545

(2) What’s the probability that Tom is given the advertising task?

There are 5 tasks and 11 board members.

Each task is assigned randomly to one person.

So the chance that Tom gets any specific task (like advertising meetings) is:

P(Tom gets that task) = 1 ÷ 11 ≈ 0.0909