Question

When a fair 6-sided dice is rolled 10 times, the resulting face values are as

follows: 1, 2, 6, 5, 5, 6, 3, 4, 5, 1. After conducting the experiment, the researcher
claims that P(5) = .30. This is an example of ______
probability.

Answer 1

This is an example of independent probability.

Explanation:

Independent events are not affected by previous events, just like the outcome of rolling a dice is not effected by the previous outcome. (The dice has no memory of any kind, what so ever!).

When two events are said to be independent of each other, meaning the probability that one event occurs in no way affects the probability of the other event occurring. Another example of an independent event is when you flip a coin. (The coin has no memory of any kind, what so ever!).

Multiplication Rule: When two events, A and B, are independent, the probability of both occurring is:

P(A and B) = P(A) · P(B)

The dice was cast 10 times. In three occasions a 5 came out, and in 7 occasions another outcome occurred. The probability of the outcome of exactly 3 times a 5 in 10 casts, can be calculated as:

P(5) =(1 / 6)^3 + (5 / 6)^7

P(5) = 0.28

P(5) = .3