Probability question (1 Viewer)

[YBK]

Hey, i have a probability question that i cant do if anyone can help me out with it, it'd be great!

An insurance company notices that of 2100 claims made for burglary only 10 % of premises had alarms and 16 % had keyed window locks. The number of claims where premises had both an alarm and keyed window locks was 156. If a claim is chosen at random and the premises had no alarm what is the probability that there were also no window locks.



thanks for any help

 

[pLuvia]

If you draw a Venn diagram, you'll see that 210 claims had only alarms, 336 claims had only window locks and 156 had both.

P(None of both)=(2100-54-156-180)/2100=0.8143

I think that's it

By the way, how's uni for you?

 

[YBK]

If you draw a Venn diagram, you'll see that 210 claims had only alarms, 336 claims had only window locks and 156 had both.

P(None of both)=(2100-54-156-180)/2100=0.8143

I think that's it

By the way, how's uni for you?

thanks man

unis cool. im doing accounting at unsw

the answer is actually 0.9048 but i dont know how to get it..

 

[ronnknee]

2100 * .1 = 210 had alarms
2100 * .16 = 336 had keyed windows
156 had both
210 - 156 = 180 had only alarms
336 - 156 = 54 had only keyed windows

2100 - 210 = 1890 had no alarms
1890 - 180 / 1890 = 0.90476...

 

[Captain Gh3y]

Let A be the claims that had an alarm and B be the claims that had a lock

|AUB| = |A|+|B|-|A∩B| = 210+336-156 = 390 claims with either an alarm or a lock

So 2100 - 390 = 1710 claims had neither
The probability of selecting at random a claim that had neither an alarm nor a lock is 1710/2100 = 0.8143

This would be the answer if the question was "what is the probability that a claim chosen at random had neither an alarm nor a lock".

But the question is "given that a claim had no alarm, what is the probability it had no lock?"

So our sample space is now 2100 - 210 = 1890, the number of claims with no alarm.
We already know 1710 claims had neither an alarm nor a lock. So the probability of a claim that had no alarm also having no lock is

1710/1890 = 0.9048

See the difference between the two questions?