certain insecticide kills 60% of all insects in laboratory experiments. A sample of 13 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.

0.0243

Step-by-step explanation:

In this question, we are asked to calculate the probability that if a certain insecticide having a particular potency rate is applied to a sample number of insects, exactly 4 will die.

Let's proceed.

The best Way around this is the use of Bernoulli trial.

Let the probability of death be p = 60/100 = 0.6

If the probability of living is q, its value would be 40/100 = 0.4

Now, let's write the Bernoulli trial equation

Probability of exactly 4 deaths will be;

13C4 * p^4 * q^9

= 715 * 0.6^4 * 0.4^9

= 0.024291311616

Let's say approximately 0.0243