Practice Problems on Probability

Problem 1 :

An urn contains 12 balls : 

3 Red, 5 Yellow and 4 Black

A- In this part we draw successfully and without replacement 3 balls from this urn.

Calculate the probability of the following :

D : the three balls are red.

E : the 3 balls have the same color.

F1 : the 3 balls red, Yellow, Black in this order .

F2 : the 3 balls are have different color.

G1: If the 3 balls are Red Red Black in this order.

G2 : If the 3 balls are 2 red and 1 Black.

H : If the 3 balls don't have the same color.

Solution :

Total number of balls = 3 Red + 5 Yellow + 4 Black

D : the three balls are red.

Three balls are red, 

3C₃ = 1

Doing simplification, we get

= 1/220

E : the 3 balls have the same color.

F1 : the 3 balls Red, Yellow, Black in this order.

P(RYB) = P(R) x P(Y) x P(B)

= (3/12) x (5/11) x (4/10)

=  1/22

F2 : the 3 balls are have different color.

G1: If the 3 balls are Red Red Black in this order.

P(RRB) = P(R) x P(R) x P(B)

= (3/12) x (2/11) x (4/10)

= 1/55

G2 : If the 3 balls are 2 red and 1 Black.

= (3C₂ x 4C₁)/12C3

= (3x4)/220

= 3/44

H : If the 3 balls don't have the same color.

= 1 - Probability of same color

= 1 - (3/44)

= 41/44