Question

A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly one insect will survive? Round your answer to four decimal places.

Answer 1

Answer:

0.1211 = 12.11% probability that exactly one insect will survive.

Step-by-step explanation:

For each insect, there are only two possible outcomes. Either they die during the experiment, or they do not. So we use the binomial probability distribution to solve this problem.

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.

A certain insecticide kills 70% of all insects in laboratory experiments.

This means that 30% survive, so $p = 0.3$

A sample of 10 insects is exposed to the insecticide in a particular experiment.

This means that $n = 10$

What is the probability that exactly one insect will survive?

This is P(X = 1).

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

$P(X = 1) = C_{10,1}.(0.3)^{1}.(0.7)^{9} = 0.1211$

0.1211 = 12.11% probability that exactly one insect will survive.