Answer to Question #127979 in Statistics and Probability for ada

Question

a) 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.

b) 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

a)

20%/100%=1/5.

1/5$\cdot$25=5 white balls.

25-5=20 black balls.

Let A be the event of getting 3 black balls.

P(A)=m/n,

m=C³₂₀=20!/3!/17!=1140,

n=C³₂₅=25!/3!/22!=2300,

Here C^k_n=n!/(k!(n-k)! is binomial coefficient.

P(A)=1140/2300=57/115.

The probability of getting 3 black balls is equal to 57/115.

b)

Let B the event that Malaysian citizen is under the age of 15.

20%/100%=1/5.

P(B)=1/5.

Let C be the event that all the three people chosen are age 15 or older.

Then P(C)=P($\overline{B}$)³

P($\overline{B}$)=1-P(B)=1-1/5=4/5

P(C)=(4/5)³=64/125

The probability that all the three people chosen are age 15 or older is equal to 64/125.