Question

1. You have three jars containing marbles as follows:

Jar 1    600 red, 400 white

Jar 2    900 blue, 100 white

Jar 3    350 green, 650 white

If you blindly select one marble from each jar, calculate the probability of obtaining each of the following combinations:

1. A red, a green, and a white
2. A red, a white, and a non-white
3. A color and two whites
4. At least one white

Answer 1

a) P ( a red, a green and a white) = (600/1000). (350/1000).(900/1000)= 0.189

note; red is only in jar 1 , green is only in jar 3 , so white is taken from only jar2

b) P( a red, a white, and a nonwhite)

= P( a red from jar 1). P(white from jar 2 and green from jar 3 or white from jar 3 and blue from jar 2)

= (0.6).{( 0.1).(0.35) +( 0.65).(0.9)} = 0.372

c)P( a color and two whites)

= P ( red from jar 1, white from jar 2 and 3)+ P ( blue from jar 2 , white from 1 and 3) + P green from jar 3, white from 1 and 2)

= (0.6).(0.1).(0.65) + (0.9). (0.4).(0.65) + (0.35).(0.4).(0.1)

= 0.287

d)P (atleast one white) = P ( one white ) + P ( 2 white ) + P (3white)

={ (0.4).(0.9).(0.35)+ (0.1)(0.6).(0.35)+(0.65).(0.9).(0.6)} + {(0.4)(0.1).(0.35)+(0.4).(0.65).(0.9)+(0.1).(0.65).(0.6)}+{(0.4).(0.1).(0.65)

=0.499