Question

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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 the 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 experimental probability of each color based on the table.

outcome | occurrences
pink. | =36
brown. | =33

Answer 1

Theoretical Probability (Pink Band) - 19/37
Their are 95 pink rubber bands (numerator) and when adding 95+90 = 185 (denominator) to get the theoretical probability you would get 95/185 which when simplified by the factor of 5 would be the same thing as 19/37.

Theoretical Probability (Brown Band) - 18/37

Their are 90 brown rubber bands (numerator) and we already know that are denominator will be 185 so we would get 90/185. This fraction is also divisible by a factor of 5 so when simplified you would get 18/37.

Experimental Probability (Pink/Brown Band) - 12/23 and 11/23

Pink Band: Their is a 36 (numerator) out of (36+33) 69 (denominator) chance of pulling a pink band so it would be written as 36/69 which is divisible by 3 and when simplified is written as 12/23.

Brown Band: Their is a 33 (numerator) out of our already known denominator 69 chance of pulling a brown band. When written as a fraction this would be 33/69 which is also divisible by 3 and when simplified 11/23.

We can conclude with this data that their is a slightly higher chance of pulling a pink rubber band compared to the experimental probability of picking a brown rubber band because we know that 12/23 > 11/23.