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A bag contains 15 blue marbles, 5 red marbles, and 11 green marbles. How many blue marbles must be removed
from the 31 marbles in the bag so that the probability of randomly drawing a blue marble is 1/3?
Answer:
7 blue marbles
Step-by-step explanation:
15 blue
5 red
11 green
Total = 31
Number of Blue marbles that must be removed to obtain a probability of :
P(blue) = 1/3
Probability = required outcome / Total possible outcomes
Let number of blue marble to be removed = x
Number of Blue becomes : 15 - x
Total becomes : 31 - x
P(blue) = 1/3
1/3 = (15 - x) / (31 - x)
1/3 * (31 - x) = 15 - x
(31 - x) / 3 = 15 - x
31 - x = 45 - 3x
-x + 3x = 45 - 31
2x = 14
x = 14 / 2
x = 7