probability問題,,,急!!!!!thank!!!

According to the provided information
No. of claims with alarms = 10% x 2,200 =220
No. of claims with keyed window locks = 2,200 x 16% =352

Among these 2,200 claims,
No. of claims with alarms and keyed window locks = 140
No. of claims with keyed window locks ONLY = 352-140 =212
No. of claims with alarm only = 220-140= 80
No. of claims with no lock and no alarm = 2,200-140-212-80
=1,768


Now let's compute probability that a claim with no window locks provided that it has no alarm

Claim with no alarm = 2,200 - 220 = 1,980
Among these 1,980 claims with no alarm,
1,768 claims with no lock and no alarm
212 claims with lock only

So the probability that a claim with no window lock provided that it has no alarm
=1768/1980
=0.8929

Of the 2200 claims, 10% of them had alarms = 220 premises
Of the 2200 claims 16% of them had keyed window locks = 352 premises.
The number of premises that had both = 2200 x 14% = 308
The number of premises that had none = 2200 - 308-220-352=1420
The probability that there were no alarm and keyed window lock is
1420/2200 = 0.645

2009-05-15 14:29:04 補充：
The number of premises that had none = 2200 - 140 - 80 - 212 = 1768
The probably that the claim had none is = 1768/2200 = 0.8036