The best way to achieve a good score on the GMAT is to master the content tested on the GMAT and practice it extensively. We sincerely believe anybody can score a 700 with enough practice and study of the content the GMAT tests.
In order to help you achieve a high score, we are pleased to provide you with a series of high-quality GMAT practice questions and detailed explanations for free. In addition, we provide a daily GMAT practice question RSS feed.
GMAT Practice Question of the Day
If E is defined to be drawing a black card out of a normal 52 card deck and F is defined to be drawing a heart, what is the probability of either E or F coming true?
Correct Answer: E
The question is asking for P(E∪F), which is technically referred to as the union of events E and F (i.e., the probability of either event E or event F coming true).
The statistical formula for this type of problem is:
P(E∪F) = P(E) + P(F) - P(E∩F)
In words: the probability of events E or F = the probability of event E + the probability of event F - the probability of both events E and F occurring simultaneously
Note: It is necessary to subtract P(E∩F) in order to avoid double counting.
P(E) = 1/2 since all cards are either black or red and, as a result, half of the cards are black.
P(F) = 1/4 since there are four types of cards (i.e., hearts, diamonds, clubs, or spades).
P(E∩F) = 0 since it is impossible to pick a card that is both black and a heart because of the fact that hearts are red cards (not black cards).
For students with a more advanced understanding of statistics, you will notice that E and F are mutually exclusive. As a result, a simpler statistical formula can be used: E and F Mutually Exclusive
Determine if E and F are mutually exclusive.
P(E∩F) = 0. It is impossible to draw a card that is both black and a heart. Thus, the two events are mutually exclusive.
P(E∪F) = P(E) + P(F)
P(E) = 1/2 as half of a deck is composed of black cards while the other half is composed of red cards.
P(F) = 1/4 as one fourth of the deck is composed of hearts.
P(E∪F) = P(E) + P(F) = 1/2 + 1/4 = 2/4 + 1/4 = 3/4
