Answer to Question #127862 in Statistics and Probability for Jack

Question

c) A box contains 25 Balls, 20% of them are white whereas the rest of them are black. A person randomly 

chooses 3 balls from the box without replacement, find the probability of getting 3 black balls. 

 (6 marks) 

d) 20% of all Malaysian citizens are under the age of 15. A company randomly chooses 3 Malaysian 

citizens (without replacement), find the probability that all the three people chosen are age 15 or older.

Answer 1

Solution c)

total balls = 25

white balls = 20% of 25 = 5

black balls = 25 - 5 = 20

Let probability of picking a black ball = p(B)

1st pick:

$$p(B) = black balls / Total balls = 20 / 25 = 0.80$$

Balls left:

black balls = 19

total balls = 24

2nd pick:

$$p(B) = 19 / 24 = 0.79167$$

Balls left:

black balls = 18

total balls = 23

3rd pick:

$$p(B) = 18 / 23 = 0.78261$$

Hence probability of picking 3 black balls without replacement:

$$= 0.8 * 0.79167 * 0.78261$$

Answer: 0.4957

Solution d)

population under 15 years = 20%

population 15 years or more = 80%

p(age > 15) = 0.8

This is the population proportion. Hence the probability of selecting a person without replacement remains the same for each trial

1st pick: p(age > 15) = 0.8

2nd pick: p(age > 15) = 0.8

3rd pick: p(age > 15) = 0.8

The probability that 3 people chosen from the population are 15 years or more:

$$=0.8 * 0.8 * 0.8$$

Answer: 0.512