For a single roll of two dice, are rolling a sum of 6 and rolling doubles independent events? Explain.

Answer 1

A -> Rolling a sum of 6 (Can occur with (1,5), (5,1), (3,3), (2,4), (4,2)
B -> Rolling Doubles (Can occur in 6 different ways)

P(A) = 5/36
P(B) = 6/36 = 1/6
P(A)*P(B) = (5/36)*(1/36)
= 5/1296

P(A∩B) = 1/36 (This only happens when (3,3) is rolled

In this case,
P(A)*P(B) =/= P(A∩B)
Hence, they are not independent, which means that their occurence affects the others' probability.

Answer 2

Ten preschool children on a playground were asked to guess their mother’s age. Calculate the mean, median, and mode of their guesses.
39, 19, 34, 57, 100, 7, 44, 18, 25, 19