Question

Which of the following are independent trials?

a. All of these answers are correct.

b. The results of a coin flip after rolling two dice and the first character of a license plate and the color of the car.

c. The results of a coin flip after rolling two dice

d. The first character of a license plate and the color of the car

e. The total of two dice after recording the value of the first die rolled

Answer 1

Two trials are independent if the outcome of one of them doesn't depend on the other one.

Lets begin with option (e): The total of two dice after recording the value of the first die rolled.

Here, we can see that the total depends upon the number that was obtained on the first die. Hence, it is dependent on the first die. Thus, we can say that these are dependent trials.

option(d): The first character of a liscence plate and color of the car.

It is obvious that the first character of the liscence plate doesn't affect the color of the car in any way as it has no relation with it. Hence these are independent trials.

option (c): The results of a coin flip after rolling two dice.

The outcomes of rolling of two dice is not related to the results of the coin flip in any way as both of them are separate entities. Hence these are independent trials.

Hence both option(d) and option(c) are independent events.

Hence the correct answer is :

b) The results of a coin flip after rolling two dice and the first character of a license plate and the color of the car.