Question: A bag contains 7 red, 9 yellow, and 3 black balls. If a ball is picked at random, what is the probability that the ball drawn will be either a red or a black ball?

1. \(\frac{7}{19}\)
2. \(\frac{9}{19}\)
3. \(\frac{10}{19}\)
4. \(\frac{11}{19}\)
5. \(\frac{12}{19}\)

Answer:

Approach Solution (1):

Probability of A or B can be written as:
P (A or B) = P (A) + P (B) – P (A and B)

Given that:-

Total balls = 19
Probability of choosing a red ball =\(\frac{7}{19}\)P (A)
Probability of choosing a black ball =\(\frac{3}{19}\)P (B)

Probability of choosing a black and a red ball = 0 (not possible as it either be red or black)
So, P (A or B) =\(\frac{7}{19}\)+\(\frac{3}{19}\)- 0 =\(\frac{10}{19}\)

Correct Option: C

Approach Solution (2):

From the question, we can see that
Total possible of outcomes = 19

Number of possibilities for choosing a red ball = 7
Number of possibilities for choosing a black ball = 3
Number of possibilities for choosing a red ball and a black ball = 0
So, desirable outcomes = 7 + 3 + 0 = 10

Therefore, Probability =\(\frac{10}{19}\)

Correct Option: C

“A bag contains 7 red, 9 yellow, and 3 black balls. If a ball is picked at random, what is the probability that the ball drawn will be either a red or a black ball?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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