a bag contains 9 red marbles and 4 blue marbles. how many clear marbles should be added to the bag so the probibility of drawing a red marble is 3/5?????
let the number of clear marbles added be x
so prob of drawing a red
= 9/(13+x)
9/(13+x) = 3/5
39 + 3x =45
3x= 6
x = 2
2 clears should be added
check:
now the number of marbles would be 15
(9 red, 4 blue, 2 clear)
prob of a red = 9/15 = 3/5
To find out how many clear marbles should be added to the bag, we need to understand the concept of probability and ratios.
Let's start by determining the total number of marbles in the bag, including the red and blue marbles. There are 9 red marbles and 4 blue marbles, so the total number of marbles is 9 + 4 = 13.
Now, we need to calculate the desired probability of drawing a red marble after adding clear marbles. The probability of drawing a red marble can be expressed as the number of red marbles divided by the total number of marbles, or (9 + x)/(13 + x), where x represents the number of clear marbles added.
According to the given information, the desired probability is 3/5. So we can write the equation as follows:
(9 + x)/(13 + x) = 3/5
To solve this equation, we can cross-multiply and simplify:
5(9 + x) = 3(13 + x)
45 + 5x = 39 + 3x
2x = 39 - 45
2x = -6
x = -6/2
x = -3
We obtained a negative value for x, which doesn't make sense in this context, as the number of clear marbles cannot be negative. Therefore, it is not possible to add clear marbles to the bag to achieve a probability of 3/5 for drawing a red marble.