Question

bag contains 3 red, 4 blue, 4 yellow, and 5 green marbles. Only yellow marbles will be added to the bag. Question How many yellow marbles should be added to the bag to make the probability of choosing a yellow marble 1-third? Enter the answer in the box.

Answer 1

Additional yellow marbles to make the probability 1/3

= 2 yellow marbles

Explanation:

Let x represent the number of yellow marbles added
There are already 4 yellow marbles

If we add x marbles:
Number of yellow marbles increases by x => 4 + x

Total number of marbles before adding yellow marbles = 3 + 4 + 4+5= 16
After adding x yellow marbles, total number of all marbles= 16 + x

P(choosing one yellow marble)
= Number of yellow marbles/Total number

`= (4+ x)/(16 + x)`

We want this probability to be 1/3

`(4+ x)/(16 + x) = (1)/(3)`

Cross multiply

`(x + 4) \cdot 3 = (x + 16)\cdot 1\\ 3x + 12 =x + 163x - x = 16 - 12\\2x = 4\\x = 2\\`

Verify
After adding 2 yellow marbles, there are 4 + 2 = 6 yellow marbles

Total number of marbles = 16 + 2 = 18

P(yellow) = 6/18 = 1/3