aj5105 wrote:If the probability that event A will occur is 0.5, what is the probability that event B will occur?
(1) The probability that both A and B will occur is 0.3.
(2) The probability that at least one of the events will occur is 0.8.
This doesn't seem much like a real GMAT probability question, but since the question doesn't mention whether A and B are independent events, you have a lot less information here than you might think at first. The solution in the original post was correct; the others are not. In all of the solutions that followed the first, people have assumed that the events were *independent*. That is the only scenario when you can safely use the formula P(A AND B) = P(A)*P(B). If the events are not independent, that formula doesn't apply. It's easy to illustrate why neither statement is sufficient with a simple real world example:
Suppose you have ten cards, numbered from 1 to 10. You pick one card. Let A be "the number on the card is odd". Then the probability of A is 0.5.
If B is "the number on the card is less than 7", then there is a 0.3 chance that A and B both occur. If instead B is "the number on the card is less than 6", then there is also a 0.3 chance that A and B both occur. So 1) cannot be sufficient; the probability of B is 0.6 in the first case and 0.5 in the second case.
If B is "the number on the card is less than 7" then there is a 0.8 chance that A or B (or both) occurs. If B is "the number on the card is less than 8", there is again a 0.8 chance that A or B (or both) occurs. So 2) cannot be sufficient either.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
