Question

By observing the sample space of the die and chips, determine the probability of obtaining:

- the number 3 and the color black

- an even number and the color white

- a number less than 3 and the color white

Answer 1

I am assuming that the chip has two sides : Black and White. So, the sample space for die is {1,2,3,4,5,6} and the sample space of chip is {Black, White}. As the outcome of chip and die are independent, the probability will be multiplied by the law of indepedent events. I am also assuming that the die is unbiased, i.e probability of occurring any number in the sample space is 1/6. The same unbiasedness is true for chip.

a) P(the number 3 and the color black) = P(the number 3) * P( the color black) = 1/6 * 1/2 = 1/12

b) P(an even number and the color white) = P(an even number) * P( the color white) = 3/6 * 1/2 = 1/4

c) P(a number less than 3 and the color white) = P(a number less than 3) * P( the color white) = 2/6 * 1/2 = 1/6