Question

Suppose you do a study on the impact of chemicals in drinkwater on the health of citizens in a small town of 1000 people: 490 males, 510 females; 300 younger than 20 and 100 older than 75. 400 people are working. Every person has a unique identifier, and you randomly select 3 people to be tested. Calculate the following probabilities:

a. P(all people drawn are male)

b. P(2 of the 3 drawn are male)

c. P(all 3 are older than 75)

d. P(all 3 are younger than 20)

Answer 1

Now , the total number of ways in which 3 people can be selected out of 1000 people

  $=\binom{1000}{3}$

( These are the total number of elementary cases which are mutually exclusive , mutually exhaustive and equally likely )

a ) P ( all people drawn are male )

  $=\frac{\binom{490}{3}}{\binom{1000}{3}}=0.1173$

b ) P ( 2 of the 3 drawn are male )

  $=\frac{\binom{490}{2}\binom{510}{1}}{\binom{1000}{3}}=0.3677$

c ) P ( all 3 are older than 75 )

$=\frac{\binom{100}{3}}{\binom{1000}{3}}=0.000973$

d ) P ( all 3 are younger than 20 )

$=\frac{\binom{300}{3}}{\binom{1000}{3}}=0.0268$