Question

Suppose that Marvin rolls a pair of fair six-sided dice. Let A be the event that the first die lands on a 4 and B be the event that rolls doubles

P(A), the probability that the first die lands on 4?
P(B), the probability that Marvin rolls doubles?
P(A and B) the probability that the first die lands on 4 and Marvinv rolls doubles?
DEPENDENT OR INDEPENDENT?

Answer 1

1/6

1/6

1/36

Independent

Explanation:

Make a chart with 36 outcomes of a pair of six sided dice.

Count the amount that starts with 4, which is 6. 6/36 = 1/6

Doubles. Count the pairs, basically both numbers are the same. 6 outcomes out of total is 1/6.

Last one.

(1/6)^2 = 1/36

These are independent, because the first die landing on 4 doesn't have anything to do with making the die becoming doubles.