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?

Answer:

1 button.

Step-by-step explanation:

Total buttons = 40

Total red buttons = 6

Total Buttons removed =25

Buttons left = 40–25 = 15

Let the red buttons left = x

1.)Then, the probability of red buttons after removing 25 buttons = x/15 outcome / Total outcome)

2.)Probability of red buttons in the bag after removing 25 buttons is 1/3 (As given in the question)

Comparing Statement 1.) & 2.) , We get

x/15 = 1/3

x = 5

So the red buttons left = 5

Total red buttons= 6

Red buttons removed = 6–5= 1

Hence, only 1 button was red in the 25 removed buttons

There is only one red button in the removed buttons if it has a chance of drawing a red button from the bag after removing 25 buttons from the bag with 14 blue, 6 red, 12 green, and 8 purple buttons is 1/3. This is obtained by equating the probability of getting red buttons from the bag after removing 25 buttons with the given probability of red buttons.

Probability is the measure of the likelihood of an event occurring.

Probability is given by the ratio of the number of favorable outcomes with respect to an event to the total number of possible outcomes.

[tex]p(A) = \frac{n(A)}{n(S)}[/tex]

p(A) is the probability of event A

n(A) is the number of outcomes with respect to A

n(S) is the total number of possible outcomes

Given that a bag contains 14 blue, 6 red, 12 green, and 8 purple buttons.

So the total number of buttons in the bag = 40

It is given that 25 buttons are removed from the bag randomly

thus, the remaining buttons in the bag = 40 - 25 = 15

It is given that the probability of drawing a red button from the bag after removing 25 buttons is 1/3

So, for finding the number of red buttons in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of red buttons and p(A) = 1/3 and  n(s) = 15 (after removing)

Thus, the number of red buttons in the bag after removing = [tex]\frac{1}{3}[/tex] × 15 = 5

So, the number of red buttons left in the bag = 5

then, the red buttons removed from the bag = 6 - 5 = 1

Therefore, only 1 red button is removed from the bag.

Learn more about probability here:

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