Problem 151E

Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in 20% of its area. Each tissue is chosen from a randomly selected area on the ivy plant.

(a) What is the probability that four successive samples show the signs of infestation?

(b) What is the probability that three out of four successive samples show the signs of infestation?

Answer

Step 1 of 2

(a)

Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in of its area. Each tissue is chosen from a randomly selected area of the ivy plant.

we are asked to find the probability that four successive samples show the signs of infestation.

Let denote an infested plant sample.

Let denote the good plan sample.

We have given the probability that the ivy plant is infested is

Hence the probability that the plant is not infected or good is

The number of ways to obtain four consecutive samples showing the signs of the infestation is,

Hence the probability is,

Hence the probability that four successive samples show the signs of an infestation is