Question

A scientist has identified a number of cacti in a certain area of the Mojave Desert.
barrel cacti 45
cottontop cacti 60
prickly pears 70
What is the experimental probability that the next cactus identified will be a barrel cactus?
Write your answer as a fraction or whole number.
P(barrel cactus)=

Answer 1

To find the experimental probability of selecting a barrel cactus, you can use the formula for probability:

\[
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes is the number of barrel cacti, which is 45. The total number of cacti identified is the sum of all cacti:

\[
\text{Total} = \text{barrel cacti} + \text{cottontop cacti} + \text{prickly pears} = 45 + 60 + 70 = 175
\]

Thus, the probability of identifying a barrel cactus is:

\[
P(\text{barrel cactus}) = \frac{45}{175}
\]

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:

\[
P(\text{barrel cactus}) = \frac{45 \div 5}{175 \div 5} = \frac{9}{35}
\]

The experimental probability that the next cactus identified will be a barrel cactus is:

\[
P(\text{barrel cactus}) = \frac{9}{35}
\]