Question

A closed box with a hole in one corner contains coloured marbles: 4 are red, 2 are blue, 3 are white and 1 is green. The box is shaken and 1 marble falls out. Its colour is recorded and it is placed back in the box. This is done 200 times. a. How many times is a red or blue marble expected to fall out of the box after 200 trials? b. How many times is a marble that has a colour other than white expected to fall out of the box after 200 trials?

Answer 1

Total number of marbles: 4+2+3+1 = 10

(a)

Out of 10 marbles 4+2 = 6 are red or blue. Since marbles are drawn with replacement so the probability of getting a red or blue marbles remain same each time. So probability of success in each trial is:

p = 6 /10 = 0.60

The expected number of times red or blue marble fall out of the box after 200 trials is

np = 200 * 0.60 = 120

(b)

Out of 10 marbles 4+2 +1= 7 are other than white. Since marbles are drawn with replacement so the probability of getting marble other than white remain same each time. So probability of success in each trial is:

p = 7/10 = 0.70

Number of times is a marble that has a colour other than white expected to fall out of the box after 200 trials is

np = 200 * 0.70 = 140