A bag contains two dice, A and B . Die A is a standard fair die with faces numbered 1, 2, 3, 4, 5, 6 . Die B is a modified fair die with faces numbered 2, 2, 4, 4, 6, 6 . A die is randomly selected from the bag and rolled three times. The probability that the numbers obtained on the three rolls form a strictly increasing sequence is

Step-by-step solution

Let E₁ be the event that die A is selected, and E₂ be the event that die B is selected. Since a die is chosen randomly, P(E₁) = P(E₂) = 1 2 . Let E be the event that the numbers obtained on the three rolls form a strictly increasing sequence. If die A is selected: Total outcomes for 3 rolls = 6³ = 216 . For a strictly increasing sequence, we must choose 3 distinct numbers from 1, 2, 3, 4, 5, 6 , which can be done in ⁶C₃ = 20 ways. Each choice corresponds to exactly one strictly increasing sequence. P(E | E₁) = 20 2