GMAT Focus EditionQuantitative ReasoningMedium
A box contains 5 red balls, 3 blue balls, and 2 green balls. If two balls are drawn randomly from the box without replacement, what is the probability that both balls are red?
- A1/10
- B2/9
- C1/4
- D5/18
Show answer & explanationAnswer & explanation
Correct answer: B. 2/9
Total balls = 5 + 3 + 2 = 10. The probability of drawing the first red ball is 5/10. After drawing one red ball, there are 4 red balls left and 9 total balls. The probability of drawing a second red ball is 4/9. The probability of both events occurring is (5/10) * (4/9) = (1/2) * (4/9) = 4/18 = 2/9.
Why the other options are wrong
- A. This is incorrect; it might be the probability of drawing one red ball if there were 10 of them, or an error in calculation.
- C. This is incorrect; it might be the probability of drawing one red ball (5/10 = 1/2) squared, which assumes replacement.
- D. This is incorrect; it might be a result of algebraic error or miscalculation.
Conditional Probability (Without Replacement)
The probability of an event occurring given that another event has already occurred, where the first event changes the conditions for the second event (e.g., by reducing the sample space).
- The denominator (total possible outcomes) decreases after each draw.
- The numerator (favorable outcomes) also decreases if the drawn item is of that type.
- Calculated by multiplying the probabilities of successive events.
Memory trick: Each pick changes the 'pie' for the next slice.