SOLUTION: Please answer the following questions and explain how you derived each of your answer. Three students work independently on a homework problem. The probability that the first

Question 244669: Please answer the following questions and explain how you derived each of your answer.
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 by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please answer the following questions and explain how you derived each of your answer.
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?
Since the events are independent, P(all solve) = 0.95*0.85*0.80
= 0.646
---------------------------
b. What is the probability that the first student solves the problem and the other two students do not?
0.95*0.15*0.20 = 0.0285
---------------------------
c. What is the probability that none of the three students solves the problem?
0.05*0.15*0.20 = 0.0015
==============================
Cheers,
Stan H.
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