In three independent flips of a coin where there is a 55 % chance of flipping a tail , let A denote {first flip is a tail }, B denote {second flip is a tail }, C denote {first two flips are tail s}, and D denote {three tails on the first three flips}. Find the probabilities of A, B, C, and D, and determine which, if any, pairs of these events are independent.

Pr (A) = 0.55

Pr (B) = 0.55

Pr (C) = 0.3025

Pr (D) = 0.166375

Step-by-step explanation:

Given that:

Pr (tail) = 55% = 0.55

Pr (head) = 1 - Pr (tails)

Pr (head) = 1 - 0.55

Pr (head) = 0.45

Pr (A) = first flip is a tail = 0.55

Pr (B) = second flip is a tail

Pr (B) = Pr (head on the first flip and tail on the second flip) + P (tail on both flips)

Pr (B) = (0.45 * 0.55) + (0.55 * 0.55)

Pr (B) = 0.2475 + 0.3025

Pr (B) = 0.55

Pr (C) = 0.55 x 0.55

= 0.3025

Pr (D) = 0.55 x 0.55 x 0.55

= 0.166375

From above; we can conclude that Pr (A) and Pr (B) are independent.