A bag holds 3 yellow marbles and 7 blue marbles. how many and what color marbles could you add to the bag so that the probability of picking a yellow marbles is 1/4?
3 * 4 = 12
12 - 10 = ? more blue marbles
2 more blue marbles
To find out how many and what color marbles you could add to the bag, let's start by determining the total number of marbles in the bag currently.
The bag currently holds 3 yellow marbles and 7 blue marbles. So, the total number of marbles in the bag is 3 + 7 = 10.
Next, let's denote the number of marbles to be added as 'x'.
If 'x' yellow marbles are added, then the total number of yellow marbles becomes 3 + x.
Similarly, the total number of marbles, including the added marbles, becomes 10 + x.
We want the probability of picking a yellow marble to be 1/4. Probability is defined as the number of favorable outcomes divided by the number of possible outcomes.
So, the probability of picking a yellow marble would be: (3 + x) / (10 + x) = 1/4.
To solve this equation, we can cross-multiply:
4(3 + x) = 1(10 + x)
12 + 4x = 10 + x
3x = -2
x = -2/3
We obtained a negative value for 'x', which does not make sense in this context. Therefore, there is no real solution to this problem.
In other words, you cannot add any marbles to the bag in such a way that the probability of picking a yellow marble is exactly 1/4.