Enter your answer and show all the steps that you use to solve this problem in the space provided. Write your final fraction in simplest form.
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.
Find the theoretical probability of selecting a pink rubber band.
Find the theoretical probability of selecting a brown rubber band.
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
Theoretical probability of selecting a pink rubber band:
There are a total of 95 + 90 = 185 rubber bands in the box. The probability of selecting a pink rubber band is the number of pink rubber bands in the box divided by the total number of rubber bands:
95/185
Theoretical probability of selecting a brown rubber band:
Following the same reasoning as before, the probability of selecting a brown rubber band is the number of brown rubber bands in the box divided by the total number of rubber bands:
90/185
Experimental probability of selecting a pink rubber band:
Out of the 36 + 33 = 69 total selections recorded in the table, 36 were pink rubber bands. The experimental probability of selecting a pink rubber band is the number of times a pink rubber band was selected divided by the total number of selections made:
36/69 = 12/23
Experimental probability of selecting a brown rubber band:
Out of the 69 total selections recorded in the table, 33 were brown rubber bands. The experimental probability of selecting a brown rubber band is the number of times a brown rubber band was selected divided by the total number of selections made:
33/69 = 11/23
Final answers:
Theoretical probability of selecting a pink rubber band: 95/185 (or 19/37 in simplest form)
Theoretical probability of selecting a brown rubber band: 90/185 (or 18/37 in simplest form)
Experimental probability of selecting a pink rubber band: 12/23 (cannot be simplified any further)
Experimental probability of selecting a brown rubber band: 11/23 (cannot be simplified any further)