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:
[tex]P(X=x)=\ ^nC_xp^x(1-p)^{n-x}[/tex], where x= number of successes , p=probability of success in each trial, n= sample size.
The probability that exactly 2 insects will survive = [tex]^{14}C_2(0.20)^2(0.80)^{12}[/tex]
[tex]\\\\=\dfrac{14!}{2!12!}(0.04)(0.068719476736)\\\\=0.2501[/tex]
Hence, the probability that exactly 2 insects will survive = 0.2501
