Question

Three students work independently on a homework problem.

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