Question

Imagine that in an important match of Premier League 4 of 22 footballers have used drugs and five of them are randomly tested for the use of drugs, what is the probability that :

a) one of the 4 footballers who have used drugs will be included in the tests;

b) two of the 4 footballers who have used drugs will be included in the tests;

c) three of the 4 footballers who have used drugs will be included in the tests;

d) the 4 footballers that have used drugs will be included in the tests?

Answer 1

(a)

Population:

Footballers who used drugs = 4

Footballers who did not use drugs = 18

Total footballers = 22

Sample:

Footballers who used drugs = 1

Footballers who did not use drugs = 4

Total footballers = 5

Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334

Number of ways of selecting 1 Footballer who used drugs from 4 Footballers who used drugs = 4C1 = 4

Number of ways of selecting 4 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C4 = 3060

So,

the probability that :one of the 4 footballers who have used drugs will be included in the tests = (4 X 3060)/26334 = 0.4648

So,

Answer is:

0.4648

(b)

Population:

Footballers who used drugs = 4

Footballers who did not use drugs = 18

Total footballers = 22

Sample:

Footballers who used drugs = 2

Footballers who did not use drugs = 3

Total footballers = 5

Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334

Number of ways of selecting 2 Footballer who used drugs from 4 Footballers who used drugs = 4C2 = 6

Number of ways of selecting 3 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C3 = 816

So,

the probability that :two of the 4 footballers who have used drugs will be included in the tests = (6 X 816)/26334 = 0.1859

So,

Answer is:

0.1859

(c)

Population:

Footballers who used drugs = 4

Footballers who did not use drugs = 18

Total footballers = 22

Sample:

Footballers who used drugs = 3

Footballers who did not use drugs = 2

Total footballers = 5

Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334

Number of ways of selecting 3 Footballer who used drugs from 4 Footballers who used drugs = 4C3 = 4

Number of ways of selecting 2 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C2 = 153

So,

the probability that :three of the 4 footballers who have used drugs will be included in the tests = (4 X 153)/26334 = 0.0232

So,

Answer is:

0.0232

(d)

Population:

Footballers who used drugs = 4

Footballers who did not use drugs = 18

Total footballers = 22

Sample:

Footballers who used drugs = 4

Footballers who did not use drugs = 1

Total footballers = 5

Number of ways of selecting 5 Footballers from 22 Footballers = 22C5 = 26334

Number of ways of selecting 4 Footballer who used drugs from 4 Footballers who used drugs = 4C4 = 1

Number of ways of selecting 1 Footballer who did not use drugs from 18 Footballers who did not use drugs = 18C1 = 18

So,

the probability that :four of the 4 footballers who have used drugs will be included in the tests = (1 X 18)/26334 = 0.0007

So,

Answer is:

0.0007