In a bag there are 7 red tiles, 3 blue tiles, and 2 purple tiles. How many and what color tiles would you have to add to the bag so that the probability of picking red is 1/3?
you want red to be 1/3, you have 7 to choose from, so you want probability to be 7/21. YOu have 12, how many more non red tiles would you add to make 21?
12 in bag now
7/12 are red which is more than 1/3
Say we add x blue tiles
then
7/(12+x) = 1/3
12 + x = 21
x = 9
so add 9 blue tiles for example
check
7 red
12 blue
2 purple
that is 21 total
7/21 = 1/3 check
To find out how many and what color tiles need to be added to the bag in order for the probability of picking a red tile to be 1/3, we first need to determine the total number of tiles in the bag before any additional tiles are added.
The initial number of red tiles is 7, blue tiles is 3, and purple tiles is 2, making a total of 7 + 3 + 2 = 12 tiles in the bag.
Let's assume we add x number of tiles to the bag. To have a probability of 1/3 of picking a red tile, the number of red tiles should be one-third of the total number of tiles in the bag after adding the new tiles.
This can be represented as:
(red + x) / (total + x) = 1/3
Substituting the known values:
(7 + x) / (12 + x) = 1/3
To solve this equation, we can cross-multiply:
3(7 + x) = 1(12 + x)
Simplifying the equation:
21 + 3x = 12 + x
Combining like terms:
2x = -9
Dividing both sides by 2:
x = -9/2
This result tells us that we need to add -9/2 tiles to the bag, which does not make sense as we cannot have a fraction of a tile. Therefore, there is no whole number of additional tiles that can be added to the bag to achieve a probability of picking a red tile equal to 1/3.
In conclusion, it is not possible to add a whole number of tiles to the bag in order to achieve a probability of picking a red tile equal to 1/3.