Question

There are four blue balls, three red balls, three yellow balls, and two green balls in a basket.

a.) With your eyes closed, you reach into the basket and choose a single ball. What is the probability that it is blue?

b.) Now instead you chose balls and replace them until a red ball appears. What is the probability a red ball appears for the first time on the 10th draw?

c.) Now you choose balls and replace them until a red or yellow ball is chosen. What is the probability that neither a red nor a yellow ball will be chose in 25 draws?

Answer 1

Total number of balls = 4+3+3+2 = 12

a) P(blue ball) = Number of blue balls / Total number of balls

= 4/12

= 1/3

b) P(red ball) = 3/12

= 0.25

P(not a red ball) = 1 - 0.25

= 0.75

P(a red ball appears for the first time on the 10th draw) = P(first 9 balls are not red) x P(10th ball is red)

= 0.75⁹ x 0.25

= 0.0188

c) P(red or yellow ball) = 6/12

= 0.5

P(not a red or yellow) = 1 - 0.5

= 0.5

P(neither a red nor a yellow ball will be chose in 25 draws) = 0.5²⁵

= 2.98x10^-8