SOLUTION: Alice and Bob work on a math problem independently. The probability that Alice solves the problem is 0.8 and the probability that Bob solves it is 0.6. (a) What is the probabilit

Question 403748: Alice and Bob work on a math problem independently. The probability that Alice solves the
problem is 0.8 and the probability that Bob solves it is 0.6.
(a) What is the probability that both solve the problem?
(b) What is the probability that neither solves it?
(c) What is the probability that exactly one of them solves it?
(d) Given that exactly one of them solves the problem, what is the probability that it is
Bob?
A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.
Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that
the 20 bulbs are independent of each other.
What is the probability that the string of lights will go out during the holidays?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Alice and Bob work on a math problem independently. The probability that Alice solves the problem is 0.8 and the probability that Bob solves it is 0.6.
(a) What is the probability that both solve the problem?:0.6*0.8
------------------------------
(b) What is the probability that neither solves it?:0.4*0.2
------------------------------
(c) What is the probability that exactly one of them solves it?
Ans: 1 - [0.48+0.08] = 0.44
---------------------------------
(d) Given that exactly one of them solves the problem, what is the probability that it is Bob?
Ans: P(Bob|one solves) = P(Bob AND one solves)/P(one solves)
= (0.6*0.2)/0.44 = 0.27
-----------------------------------
A string of Christmas lights has 20 bulbs and if any bulb fails then the whole string goes out.
Suppose that each bulb has a 5% chance of failure during the Christmas holidays and that the 20 bulbs are independent of each other.
What is the probability that the string of lights will go out during the holidays?
P(failure) = 0.05
P(not fail) = 0.95
Ans: P(string out) = 1 - P(none fail) = 1-0.95^20 = 0.6415
===========================
Cheers,
Stan H.
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