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

Answer:  The below explanation proves that given probabilities are independent.

Step-by-step explanation:

Two events are said to be independent of each other, when  the probability that one event occurs in no way affects the probability of the other event occurring.

Here, bag contains 5 white marbles and 5 blue marbles.

That is, the probability that a white marble the first time,

$P(W)= \frac{5_C_1}{10_C_1} = \frac{5}{10}= \frac{1}{2}$

Since, their is a replacement occurs,

Therefore total number of marbles is again 10.

Therefore, he probability that a Red marble the second time,

$P(R)= \frac{5_C_1}{10_C_1} = \frac{5}{10}= \frac{1}{2}$

Thus, the probability of occurrence of a Red marble  is not affected by occurrence of the probability that we get white marble in first attempt.

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