Jack likes to go fishing. While waiting for the fishes to bite, he formulates the following model for the process: fishes bite according to a Poisson process with intensity 4 bites per hour. Biting fishes are caught independently, and on average only one in two times.
a) What is the probability that six fishes bite during the first two hours?
b) What is the probability that he fails to catch any fishes during the first two hours?
c) What is the probability that, during the first two hours, six fishes bite and two of these are caught?

a) 0.122

b) 3.35 × 10⁻⁴

c) 0.1071

Step-by-step explanation:

Here we have the Poisson process given by

Where:

λ = Rate = 4 bites/hour and

t = Length of time that is

Mean = λt

Where k = 6 fishes bites and t = 2 hours we have

b) The probability that he fails to catch any fishes during the first two hours is the probability t that he catches 0 fish as follows

(c) Here we have

For 1 fish caught in two times we have first time no fish and second time he caches a fish gives

0.122×(1-0.122) = 0.1071

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

step-by-step explanation: