What is the probability that the college experiences a decrease in enrollment and an increase in their cost to provide services?
Understand the Problem
The question is asking us to calculate the probability of two independent events happening together: a decrease in enrollment and an increase in the cost to provide services. We are given the probabilities of each event occurring separately, and since the events are independent, we can multiply their probabilities to find the probability of both events occurring.
Answer
$0.03$
Answer for screen readers
$0.03$
Steps to Solve
- Identify the probabilities of each independent event.
The probability of decreased enrollment is $P(E) = 0.15$. The probability of increased cost is $P(C) = 0.20$.
- Calculate the probability of both events occurring.
Since the events are independent, the probability of both occurring is the product of their individual probabilities: $P(E \text{ and } C) = P(E) \times P(C)$
- Substitute the given probabilities into the equation and solve.
$P(E \text{ and } C) = 0.15 \times 0.20 = 0.03$
$0.03$
More Information
The probability of both decreased enrollment and increased cost occurring is $0.03$, or $3%$.
Tips
A common mistake is to add the individual probabilities instead of multiplying them. This is incorrect because it doesn't account for the independence of the events. Remember, you only multiply probabilities when events are independent.
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