Question

Out of 60 applicants to a university, 40 are from the East. If 20 applicants are to beselected at random, find the probability that:

a. 10 are from East.
b. Not more than 2 are from East.

Answer 1

a. 40С10 * 20С10 / 60С20

b. 1 + (40)(20) + (40C2)(20C2) / 60С20

Explanation:

Total number of application = 60

Total number of application from east = 40

Total number of application remaining = 20

Number of ways of selecting 20 applicant = 60C20 (Sample space)

a. Probability of 10 are from East.

= (10 from east) * (10 from remaining)

= 40С10 * 20С10 / 60С20

b. Probability of Not more than 2 are from East.

= P(x≤2)

= P(x=0) + P(X=1) + P(X=2)

= [40С0 * 20С20 / 60С20] + [40С1 * 20С19 / 60С20] + [40С2 * 20С18 / 60С20]

= 1 + (40)(20) + (40C2)(20C2) / 60С20