Question

Question 5 (1 point)

Box1: 5 green balls, 4 red balls, 5 blue balls

Box2: 0 green balls, 4 red balls, 7 blue balls

Experiment: Select one of the two boxes with uniform random probability, and draw two balls from the selected box. Record the box number as the r.v. i, and the colors of the two balls as b₁, b₂.

Compute P(b₁ = green )

[Round to 3 digits after decimal point]

Your Answer:

Answer 1

Probability of selection of Box 1 = 1/2

Probability of selection of Box 2 = 1/2

There are two cases -

• Case I : Box 1 is selected

Number of balls in Box 1 = 14 (5 green , 4 red , 5 blue)

Number of ways of drawing two balls from the box = 14C2 = 91

There are 2 sub - cases

First ,

Probability of drawing two balls (1 green and 1 of any other colour ) = (5C1 x 9C1) / 14C2

= 45 / 91

Second ,

Probability of drawing 2 green balls = 5C2 / 14C2 = 10/91

Probability that b1 = green = (45/91) + (10/91) = 55/91 = 0.604

Total probability , P(b1 = green) = (0.5 x 0.604) = 0.302

• Case II : Box 2 is selected

Number of balls in Box 2 = 11 (0 green , 4 red , 7 blue)

Since , there is no green ball

probabiliy , P(b1 = green) = 0

Therefore ,

P(b1 = green) = 0.302