Data Sufficiency

The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

1) Event A and event B are independent.
2) The probability that neither event A nor event B occurs is 0.32.


* The answer will be posted in two days.

Max@Math Revolution wrote:The probability that event A occurs is 0.4 and the probability that event B occurs is 0.8. What is the probability that event A occurs but not event B?

1) Event A and event B are independent.
2) The probability that neither event A nor event B occurs is 0.32.


* The answer will be posted in two days.

I'm confused. How can the probability that event b occurs be 0.8? This implies the probability that event B doesn't occur is 0.2. Yet, we're told in statement (2) that the probability that neither event A nor event B occurs be 0.32? How can the probability of NOT A AND NOT B be greater than the probability of NOT B alone?

You only have to find out P(A∩B) in the original condition. Hence, there is only 1 variable, which means D is likely the answer. Using the condition 1) and the condition 2), we can see that the condition 1) is essentially the same as the condition 2) (1)=2)). So, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.