***I provided the correct answers given by my professor, but I am having a hard
ID: 3275311 • Letter: #
Question
***I provided the correct answers given by my professor, but I am having a hard time getting to the answers, so please be elaborate, thank you.***
A small brewery has two bottling machines. Machine A produce 75% of the bottles, and machchine B produces the rest. One out of every 20 bottles filled by A is rejected for some reason and one out of every 30 bottles from B is rejected.
a) What is the proportion of all bottles are produces by machine B? (ans:0.25)
b) What is the conditional probability that a randomly selected bottle is rejected given that it was produced by machine A? (ans:0.05)
c) What is the probability that a randomly selected bottle was both rejected and produced by machine A? (ans: 0.0375)
d) What proportion of all bottles are rejected? (ans: 0.0458)
e) What is the probability that a randomly selected bottle comes from machine A given that it was rejected? (ans: 0.8182)
Explanation / Answer
A small brewery has two bottling machines. Machine A produce 75% of the bottles, and machchine B produces the rest. One out of every 20 bottles filled by A is rejected for some reason and one out of every 30 bottles from B is rejected
a. B produces = ?, We know there are 2 bottling machines and A produces 75% of the bottles. So,
B produces 100% - 75% = 25% of the bottles
b.P( reject given A) = ? 'One out of every 20 bottles filled by A is rejected for some reason'
So, answer = (1/20) = .05
c. probability that a randomly selected bottle was both rejected and produced by machine A
=?
=P( select a bottle randomly from A)*P( reject A)
= (3/4)*(1/20) = .0375
d. Prop rejected = ?
P(bottles by A)*P(reject by A)+P(bottles by A)*P(reject by A)
=(3/4)*(1/20)+(1/4)*(1/30)
=.0458
e. probability that a randomly selected bottle comes from machine A given that it was rejected = ?
= P( reject from B given it was bottles by B) /P( reject from B given it was bottles by B) +P( reject from A given it was bottles by A)
= (3/4)*(1/20)/ (3/4)*(1/20)+(1/4)*(1/30)
=.8182
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