A box contains 95 pink rubber bands and 90 brown rubber bands. You select a rubber band at random from the box. Find each probability. Write the probability as a fraction in simplest form.
a. Find the theoretical probability of selecting a pink rubber band.
b. Find the theoretical probability of selecting a brown rubber band.
c. You repeatedly choose a rubber band from the box, record the color, and put the rubber band back in the box. The results are shown in the table below. Find the experimental probability of each color based on the table.
Outcome Occurrences
Pink 36
Brown 33
a. The theoretical probability of selecting a pink rubber band is:
P(pink) = number of pink rubber bands / total number of rubber bands = 95/185 = 19/37
b. The theoretical probability of selecting a brown rubber band is:
P(brown) = number of brown rubber bands / total number of rubber bands = 90/185 = 18/37
c. The experimental probability of selecting a pink rubber band is:
P(pink) = number of occurrences of pink rubber bands / total number of occurrences = 36/(36+33) = 36/69 = 12/23
The experimental probability of selecting a brown rubber band is:
P(brown) = number of occurrences of brown rubber bands / total number of occurrences = 33/(36+33) = 33/69 = 11/23