Md.Nazrul Islam wrote:what is the probability that event E or event F or both will occur .
1)The probability that event E will occur is 0.6
2)The probability that event F will occur is 0.4
Hello!
I see that you're fairly new to the forums, so just a friendly tip - please post your questions in the right place! This is the problem solving forum, but this is a data sufficiency question.
Data sufficiency is a test of your knowledge of concepts, NOT your ability to do lots and lots of calculations. Applying common sense and a tiny bit of math knowledge allows us to answer this question quickly and confidently without resorting to any calculations at all.
Step 1 of the Kaplan Method for DS is to analyze the question stem. Too many people just rush into the statements without enough of an understanding of the question itself, often wasting valuable time on unnecessary work.
Q: what's the probability that one or both of two events will occur.
Analysis: we need information about both events - either the probabilities that they will or will not occur.
(1) P(E); nothing about P(F), so insufficient - eliminate A and D.
(2) P(F); nothing about P(E), so insufficient - eliminate B.
Since neither statement was sufficient alone, we have to combine.
Together: P(E) and P(F).
We think: with the two individual probabilities, we can answer ANY question about the two events. SUFFICIENT, choose (C).
Remember: in DS we don't care WHAT the answer is, we only care WHETHER IT'S POSSIBLE to answer the question. Don't waste your time on unnecessary calculations.
* * *
Aside #1: when you're done a DS question, it's useful to ask yourself "if this were a PS question, what would have been the quickest way to solve it?" So, let's go into "review mode" and find the best solution for this problem.
An often time-saving approach to complex probability questions is the "one minus" method. Since the sum of all probabilities is 1, we can form the equation:
Prob(what you want) = 1 - Prob(what you don't want).
In this problem, we get:
Prob(one or both events) = 1 - Prob(neither event)
Since P(E) = 0.6, P(not E) = .4
Since P(F) = 0.4, P(not F) = .6
Accordingly, Prob(neither E nor F) = .4 * .6 = .24,
and
Prob(one or both) = 1 - .24 = .76
* * *
Aside #2: there's a problem with the wording of the question that actually disqualifies it from the GMAT - nowhere does it say that events E and F are independent. We're assuming that they are, but the GMAT would never leave a question open to multiple interpretations. So, the question should have read "what is the probability that one or both of independent events E and F occur?"
