Question

Three students work independently on a homework problem: The probability that the first student solves the problem is 0.95. The probability that the second student solves the problem is 0.85. The probability that the third student solves the problem is 0.8.

A) What is the probability that either the first or the second student solves the problem?

B) What is the probability that at least one student solves the problem?

(Answer as a decimal rounded to three decimal places)

Answer 1

Given data:

The probability that the first student solves the problem ,x = 0.95.

The probability that the first student nt solves the problem ,x' = 1-0.95 =0.05

The probability that the second student solves the problem ,y= 0.85.

The probability that the second student not solves the problem ,y'=1- 0.85 = 0.15

The probability that the third student solves the problem,z= 0.8.

The probability that the third student not solves the problem,z'=1- 0.8 =0.2

the probability that either the first or the second student solves the problem p(1or2) = probability that 1st student only solve the probelm + probability second student only solve the problem

p(1or2) = x*y'*z' +x'*y*z'

p(1or2) = 0.95*0.15*0.2 +0.05*0.85*0.2

p(1or2) = 0.0285 +0.0085 = 0.037

the probability that either the first or the second student solves the problem is 0.037