Question

Suppose that Ayumi rolls a pair of fair six-sided dice. Let AAA be the event that the first die lands on 222 and BBB be the event that the second die lands on 222. Using the sample space of possible outcomes below, answer each of the following questions. What is P(A)P(A)P, left parenthesis, A, right parenthesis, the probability that the first die lands on 222? What is P(B)P(B)P, left parenthesis, B, right parenthesis, the probability that the second die lands on 222? What is P(A\text{ and }B)P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the first die lands on 222 and the second die lands on 222? Are events AAA and BBB independent?

Answer 1

1/6

1/6

1/36

yes they both indepentdent

Explanation:

Answer 2

1/6

1/6

1/36

Events A and B are independent

Explanation:

Suppose:

A = event that first die lands on 2

B = event that second die lands on 2

Sample space:

Die 1 = 1,2,3,4,5,6

Die 2 = 1,2,3,4,5,6

Sample space of both die combined is attached below

Probability = (total number of required outcomes / total number of possible outcomes)

Probability that first die lands on 2:

P(A) = 1/6

Probability that second die lands on 2:

P(B) = 1/6

Probability of A and B:

P(A and B) = 1/6 × 1/6 = 1/36

Evebts A and B are independent because, the outcome of one event does not affect the occurrence of the other event.