Question

There is a 30% chance that T'Shana's county will have a drought during any given year. She performs a

Answer 1

Answer:

75.99% probability of a drought in at least 1 of the next 4 years

Step-by-step explanation:

For each year, there are only two possible outcomes. Either there is a drought, or there is not. The probability of there being a drought in a given year is independent of other years. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

30% chance that T'Shana's county will have a drought during any given year.

This means that $p = 0.3$

4 years

This means that $n = 4$

She performs a

She performs a simulation to find the experimental probability of a drought in at least 1 of the next 4 years

Either no year has a drought, or at least one has. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$. So

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{4,0}.(0.3)^{0}.(0.7)^{4} = 0.2401$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2401 = 0.7599$

75.99% probability of a drought in at least 1 of the next 4 years