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 0.80.
a. What is the probability that all are able to solve the problem?
b. What is the probability that the first student solves the problem and the other two students do not?
c. What is the probability that none of the three students solves the problem?
Can you help me understand how to understand probability word problems..

Answer 1

Answer:

a. 0.646

b. 0.0285

c. 0.0015

Step-by-step explanation:

Please refer to the tree diagram attached at the bottom of this answer.

a. Probability P of the three of them solving the problem:

P = P(A) · P(B) · P(C) = 0.95 · 0.85 · 0.80 = 0.646

b.  Only the first one:

P = P(A) · (1-P(B)) · (1- P(C)) = 0.95 · 0.15 · 0.20 = 0.0285

c. None of them:

P = (1-P(A)) · (1-P(B)) · (1- P(C)) = 0.05 · 0.15 · 0.20 = 0.0015