Question

Suppose major earthquakes in a certain region occur independently of one another at the rateof one every ten years. Find the probability that the next major earthquake will occur between7 and 12 years from now.

Answer 1

Answer:

Therefore, the probability is P=0.5.

Step-by-step explanation:

We know that a major earthquakes in a certain region occur independently of one another at the rateof one every ten years.

We conclude that:

$f(x)=\frac{1}{10}$

We calculate the probability that the next major earthquake will occur between7 and 12 years from now. We get:

$P=\int_7^{10} \frac{1}{10}\, dx+\int_{10}^{12} \frac{1}{10}\, dx\\\\P=\frac{1}{10} [x]_7^{10}+\frac{1}{10} [x]_{10}^{12}\\\\P=\frac{1}{10}(10-7)+\frac{1}{10}(12-10)\\\\P=\frac{3}{10}+\frac{2}{10}\\\\P=0.5$

Therefore, the probability is P=0.5.