Question

Given is a box of 50 marbles, all identical except for color. The box contains 20 blue, 10 red, 14 green, and 6 yellow marbles. If a person picks out a single marble from the box without looking, what is the probability the marble will be yellow or blue?

(A) 13/25
(B) 48/22
(C) 26/22
(D) 74/33

Answer 1

The probability of drawing a yellow or blue marble from a box containing 50 marbles is found by adding the individual probabilities. With 20 blue and 6 yellow marbles, the combined probability is 26 out of 50, which simplifies to 13/25, making option (A) correct.

Step-by-step explanation:

The question is asking for the probability that a single marble picked from a box will be yellow or blue. To find this probability, we add the probability of drawing a yellow marble to the probability of drawing a blue marble, since these are independent events.

There are a total of 50 marbles, consisting of 20 blue marbles and 6 yellow marbles. Therefore, the probability of drawing a blue marble is 20 out of 50, and the probability of drawing a yellow marble is 6 out of 50.

To find the combined probability of drawing a yellow or blue marble, we simply add the two probabilities together:

• Probability of drawing a blue marble (P(Blue)) = 20 / 50
• Probability of drawing a yellow marble (P(Yellow)) = 6 / 50
• Combined probability (P(Yellow or Blue)) = P(Blue) + P(Yellow) = (20 / 50) + (6 / 50) = 26 / 50 = 13/25

Therefore, the correct option is (A) 13/25.