A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?01356
Answer: 1Explanation:Add the 14 blue, 6 red, 12 green, and 8 purple buttons to get a total of 40 buttons. If 25 buttons are removed, there are 15 buttons remaining in the bag. If the chance of drawing a red button is now 1/3, then 5 of the 15 buttons remaining must be red. The original total of red buttons was 6. So, one red button was removed.
We can start by using the concept of probability and creating an equation to solve for the number of red buttons that were removed from the bag.
Let X be the number of red buttons removed from the bag.
The total number of buttons in the bag is:
14 + 6 + 12 + 8 = 40
After removing 25 buttons, there are 15 remaining in the bag. We know that the chance of drawing a red button from the bag after the 25 buttons are removed is now 1/3. Therefore, the number of red buttons remaining in the bag is:
6 – X = (1/3) * 15
(We multiply by 15 because there are 15 buttons remaining in the bag, and the probability of drawing a red button is 1/3.)
Simplifying this equation, we get:
6 – X = 5
X = 1
Therefore, only 1 of the removed buttons was red.
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