XAT 2011 — QA & DI Question 15
Answer the following question based on the information given below.
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Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
- Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
- Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
The scheduling officer for a local police department is trying to schedule additional patrol units in each of two neighbourhoods – southern and northern. She knows that on any given day, the probabilities of major crimes and minor crimes being committed in the northern neighbourhood were 0.418 and 0.612, respectively, and that the corresponding probabilities in the southern neighbourhood were 0.355 and 0.520. Assuming that all crime occur independent of each other and likewise that crime in the two neighbourhoods are independent of each other, what is the probability that no crime of either type is committed in either neighbourhood on any given day?
Answer & solution
0.069
- B
0.225
- C
0.69
- D
0.775
- E
None of the above
Required probability = (1 – 0.418) (1 – 0.612) (1 – 0.355) (1 – 0.520) ≈ 0.069
Hence, option (a).