Question

A dice is rolled till "3" or "4" occurred.

1. Find an expected number of times we have to roll the dice till "3" or "4" occurs.

2. What is the probability that "3" or "4" occurred on the 3rd roll?

1. (0.5 points) Here we have _________________________________ distribution with parameter(s) ______________

which is equal to ________________________.

2. (0.5 points)  An expected number of times we have to roll the dice till "3" or "4" occurs means, that we have to find ___________. The formula of _________________ it equal to _______________. Thus an expected number of times we have to roll the dice till "3" or "4" occurs is equal to _________________.

3. (0.5 points) The probability that "3" or "4" occurred on the 3rd roll can be calculated _____________________________.

It is equal to ____________________.

Answer 1

1. (0.5 points) Here we have Geometric distribution with parameter p=probability of getting "3" or "4"

which is equal to 2/6=1/3.

2. (0.5 points)  An expected number of times we have to roll the dice till "3" or "4" occurs means, that we have to find E(X), where X=random variable denoting number of times we have to roll the dice till "3" or "4" occurs. The formula of E(X) it equal to

. Thus an expected number of times we have to roll the dice till "3" or "4" occurs is equal to 3.

3. (0.5 points) The probability that "3" or "4" occurred on the 3rd roll can be calculated

It is equal to 0.1481.