A bag holds 8 yellow marbles and 5 orange marbles.How many and what color marbles would you add to the bag so that the probability of picking a yellow marble is 2/3

To solve this problem, we need to calculate the number of marbles to add and their color to achieve the desired probability.

Let's start by finding the current probability of picking a yellow marble. We have 8 yellow marbles and 5 orange marbles, so the total number of marbles in the bag is 8 + 5 = 13.

The probability of picking a yellow marble can be calculated by dividing the number of yellow marbles by the total number of marbles:

Probability of picking a yellow marble = Number of yellow marbles / Total number of marbles
= 8 / 13
≈ 0.6154

To increase this probability to 2/3, we need to find the number of marbles to add and their color.

Let's denote the number of marbles to be added as 'x'.

The new probability of picking a yellow marble, after adding 'x' marbles, can be calculated by dividing the number of yellow marbles (8 + x) by the total number of marbles (13 + x):

New probability of picking a yellow marble = (Number of yellow marbles + x) / (Total number of marbles + x)
= (8 + x) / (13 + x)

According to the problem, the new probability should be 2/3. Therefore, we can set up the following equation and solve for 'x':

(8 + x) / (13 + x) = 2/3

To solve this equation, we can cross-multiply:

3(8 + x) = 2(13 + x)

Simplifying further:

24 + 3x = 26 + 2x

Subtracting 2x from both sides:

x = 2

So, we need to add 2 marbles to the bag.

Now, let's determine the color of the marbles to add. Since we want to increase the probability of picking a yellow marble, we should add yellow marbles. Therefore, the 2 marbles to be added should be yellow.

In conclusion, we need to add 2 yellow marbles to the bag so that the probability of picking a yellow marble becomes 2/3.

Since there are 5 orange, and that makes up 1/3 of the total bag, you would multiply that by 3 to get the total amount. 2/3 of that is 10 marbles. Since there are currently 8, you subtract 8 from 10, giving you 2 marbles