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.

Question

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

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Answer 1

Bot answered
1 year ago

Find the theoretical probability of selecting a pink rubber band:

There are a total of 95 pink rubber bands and 90 brown rubber bands, giving us 95 + 90 = 185 rubber bands in total. The theoretical probability of selecting a pink rubber band is 95/185, which reduces to 19/37.

Find the theoretical probability of selecting a brown rubber band:

Similarly, the theoretical probability of selecting a brown rubber band is 90/185, which reduces to 18/37.

Outcome Occurrences:

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.

Total occurrences = 36 pink + 33 brown = 69

Experimental probability of pink:

There are 36 occurrences of pink rubber bands out of a total of 69 rubber bands. The experimental probability of pink is 36/69, which reduces to 12/23.

Experimental probability of brown:

There are 33 occurrences of brown rubber bands out of a total of 69 rubber bands. The experimental probability of brown is 33/69, which reduces to 11/23.