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 occurences
pink 36
brown 33
a. The theoretical probability of selecting a pink rubber band would be:
P(pink) = number of pink rubber bands / total number of rubber bands
P(pink) = 95 / (95 + 90)
P(pink) = 19/38
b. The theoretical probability of selecting a brown rubber band would be:
P(brown) = number of brown rubber bands / total number of rubber bands
P(brown) = 90 / (95 + 90)
P(brown) = 18/38
c. The experimental probability of selecting a pink rubber band would be:
P(pink) = number of times pink was selected / total number of selections
P(pink) = 36 / (36 + 33)
P(pink) = 12/21
P(pink) = 4/7
The experimental probability of selecting a brown rubber band would be:
P(brown) = number of times brown was selected / total number of selections
P(brown) = 33 / (36 + 33)
P(brown) = 11/21
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
a. The theoretical probability of selecting a pink rubber band would be:
P(pink) = number of pink rubber bands / total number of rubber bands
P(pink) = 95 / (95 + 90)
P(pink) = 19/38
b. The theoretical probability of selecting a brown rubber band would be:
P(brown) = number of brown rubber bands / total number of rubber bands
P(brown) = 90 / (95 + 90)
P(brown) = 18/38
c. The experimental probability of selecting a pink rubber band would be:
P(pink) = number of times pink was selected / total number of selections
P(pink) = 36 / (36 + 33)
P(pink) = 12/21
P(pink) = 4/7
The experimental probability of selecting a brown rubber band would be:
P(brown) = number of times brown was selected / total number of selections
P(brown) = 33 / (36 + 33)
P(brown) = 11/21
To find the probabilities, we need to know the total number of rubber bands in the box.
a. The theoretical probability of selecting a pink rubber band is the number of pink rubber bands divided by the total number of rubber bands in the box: 95 pink rubber bands / (95 pink rubber bands + 90 brown rubber bands) = 95/185.
b. The theoretical probability of selecting a brown rubber band is the number of brown rubber bands divided by the total number of rubber bands in the box: 90 brown rubber bands / (95 pink rubber bands + 90 brown rubber bands) = 90/185.
c. The experimental probability of a certain outcome is the number of times that outcome occurs divided by the total number of trials or occurrences.
For the experiment, we have the following information:
- Pink rubber bands occurred 36 times.
- Brown rubber bands occurred 33 times.
The total number of trials or occurrences is the sum of the pink and brown occurrences: 36 + 33 = 69.
The experimental probability of selecting a pink rubber band is 36/69.
The experimental probability of selecting a brown rubber band is 33/69.
Please note that the experimental probabilities can change with more trials or occurrences.