Question

A bag contains 5 white marbles and 5 blue marbles. You randomly select one marble from the bag and put it back. Then, you randomly select another marble from the bag. Which calculation proves that randomly selecting a white marble the first time and a blue marble the second time are two independent events?

Answer 1

I'm not sure if an equation is needed. Since you put the marble back into the bag the odds are still 50/50 that you will draw either color.

If you would have left it out then it would be dependent because the ratio would change.

Answer 2

P(W) and P(B) are independent events.

Explanation:

Given : A bag contains 5 white marbles and 5 blue marbles. You randomly select one marble from the bag and put it back. Then, you randomly select another marble from the bag.

To find : Which calculation proves that randomly selecting a white marble the first time and a blue marble the second time are two independent events?

Solution :

Independent events - When the probability that one event occurs in no way affects the probability of the other event occurring.

We have given, 5 white marbles and 5 blue marbles.

`\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}`

Total number of outcomes = 5+5=10

The probability that a white marble the first time,

`P(W)=(5)/(10)= (1)/(2)`

Their is a replacement occurs,

The probability that a blue marble the second time,

`P(B)=(5)/(10)= (1)/(2)`

The probability of occurrence of a Blue marble is not affected by occurrence of the probability that we get white marble in first attempt.

Hence, P(W) and P(B) are independent events.