Question

1. A bag contains one green marble, two yellow marbles, four blue marbles, and five red marbles.

a. What is the theoretical probability of randomly drawing a blue marble from the bag?

b. If you triple the number of green, yellow, blue, and red marbles in the bag, what will be the theoretical probability of drawing a blue marble?

C. Compare your answers for part (a) and (b). Are they the same or different? Explain.

d. How many blue marbles would you need to add to the original bag of marbles to make the probability of drawing a blue marble 12 ? Explain.

Answer 1

G = 1

Y = 2

B = 4

R = 5

Probability of drawing blue = B/( G + Y + B + R)

= 4/(1 + 2 +4 + 5)

= 4/12

= 1/3

If all marbles are tripled,

Probability of blue= 3B/(3G + 3Y + 3B + 3R)

= 12/36

= 1/3

Since all balls are multiplied by the same factor, probability remains same.

To make probability of drawing a blue equal to 1/2, let total blue balls required be B1

0.5 = B1/(1 + 2 + B1 +5)

Solving, we get B1 = 8

Since we already had 4 blue balls, 4 more blue balls are required.