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06 Mar 2015, 08:45
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (02:14) correct
21%
(02:38)
wrong
based on 115
sessions
History
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Not Attempted Yet
Factory X's bulbs work for over 5000 hours in 99% of cases, whereas factory Y's bulbs work for over 5000 hours in 95% of cases. It is known that factory X supplies 60% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
A) 96.4%
B) 98%
C) 97.4%
D) 95%
E) 93.9%
A) 96.4%
B) 98%
C) 97.4%
D) 95%
E) 93.9%
06 Mar 2015, 08:57
Kudos
Bookmarks
ynaikavde
hi,
probability that the purchased bulb is from factory x=3/5 and it will work=99%..
probability that the purchased bulb is from factory y=2/5 and it will work=95%..
so the prob that the bulb will work>5000h is 3/5*(99/100)+ 2/5*(95/100)..
now is the time we can save on time by avoiding tedious calculations...
difference between the two %=4..
since the ratio of number of bulbs of x:y=60:40=3:2...
we divide this gap of 4 in 5 parts and our answer will be either 3times the difference above 95 or 2 times the difference below 99..
lets take 3 parts=3*4/5=2.4... ans =95+2.4=97.4.. ans C..
by looking at examples you can narrow down choices...
answer has to be between 95 and 99 and closer to 99 as more bulbs have 99 as probability.. so only 97.4 and 98 are left..
06 Mar 2015, 09:25
Kudos
Bookmarks
Total probability
P(A) =P)(A|B1).P(B1) +P(A|B2).P(B2)
A= bulb works
B= factory from which it was bought
P(A) =P)(A|B1).P(B1) +P(A|B2).P(B2)=\(\frac{99}{100}*\frac{60}{100}+\frac{95}{100}*\frac{40}{100}=\frac{(94 + 380)}{1000}=\frac{974}{1000}\)
where
P(B1)=60/100 is the probability that the purchased bulb was manufactured by factory X;
P(B2)=4/100 is the probability that the purchased bulb was manufactured by factory Y;
P(A|B1)=99/100 is the probability that a bulb manufactured by X will work for over 5000 hours;
P(A|B2)=95/100 is the probability that a bulb manufactured by Y will work for over 5000 hours.
Thus each purchased light bulb has a 97.4% chance to work for more than 5000 hours
Kudos if this helps
P(A) =P)(A|B1).P(B1) +P(A|B2).P(B2)
A= bulb works
B= factory from which it was bought
P(A) =P)(A|B1).P(B1) +P(A|B2).P(B2)=\(\frac{99}{100}*\frac{60}{100}+\frac{95}{100}*\frac{40}{100}=\frac{(94 + 380)}{1000}=\frac{974}{1000}\)
where
P(B1)=60/100 is the probability that the purchased bulb was manufactured by factory X;
P(B2)=4/100 is the probability that the purchased bulb was manufactured by factory Y;
P(A|B1)=99/100 is the probability that a bulb manufactured by X will work for over 5000 hours;
P(A|B2)=95/100 is the probability that a bulb manufactured by Y will work for over 5000 hours.
Thus each purchased light bulb has a 97.4% chance to work for more than 5000 hours
Kudos if this helps
