Question

A certain insecticide kills 80% 80% of all insects in laboratory experiments. A sample of 14 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 2 insects will survive? Round your answer to four decimal places.

Answer 1

Answer: The probability that exactly 2 insects will survive = 0.2501

Step-by-step explanation:

Given: A certain insecticide kills 80% of all insects in laboratory experiments.

The probability that a particular insect survives= 1-0.80=0.20

Sample size: n=14

Binomial probability distribution:

$P(X=x)=\ ^nC_xp^x(1-p)^{n-x}$, where x= number of successes , p=probability of success in each trial, n= sample size.

The probability that exactly 2 insects will survive = $^{14}C_2(0.20)^2(0.80)^{12}$

$\\\\=\dfrac{14!}{2!12!}(0.04)(0.068719476736)\\\\=0.2501$

Hence, the probability that exactly 2 insects will survive = 0.2501