Carcass wrote:
A set of marbles contains only black marbles, white marbles, and yellow marbles. If the probability of randomly choosing a black marble is 1/14 and the probability of randomly choosing a white marble is 3/4, what is the probability of randomly choosing a yellow marble?
A. 5/28
B. 3/14
C. 1/4
D. 2/7
E. 9/28
Key property: The probabilities of all possible outcomes must add to 1For this question, there are 3 possible outcomes: select a black marble, select a white marble, or select a yellow marble.
This means: P(select a black marble) + P(select a white marble) + P(select a yellow marble) = 1
Substitute given values: 1/14 + 3/4 + P(select a yellow marble) = 1
Rewrite with same denominators: 2/28 + 21/28 + P(select a yellow marble) = 28/28
Solve: P(select a yellow marble) = 28/28 - 2/28 - 21/28
So, P(select a yellow marble) = 5/28
Answer: A