Question

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 10 insects will die

Answer 1

The probability that exactly 10 insects will die

P( X = 10 ) = 0.06385

Explanation:

Step(i):-

Given a certain insecticide kills 60% of all insects in laboratory experiments

Given proportion p = 0.60

q = 1 - 0.60 = 0.40

Given sample size 'n' = 12

Step(ii):-

Let "X' be the random variable of binomial distribution

`P(X=r) = n_{C_(r) } p^(r) q^(n-r)`

The probability that exactly 10 insects will die

`P(X=10) = 12_{C_(10) } (0.60)^(10) (0.40)^(12-10)`

`n_{C_(r) } = (n!)/((n-r)!r!) = (12!)/((12-10)!10!) = 66`

`P(X=10) = 66 X (0.60)^(10) (0.40)^(2) = 0.06385`

Final answer:-

The probability that exactly 10 insects will die

P( X = 10 ) = 0.06385