Question

A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die. Select the correct answer from above options

Answer 1

Given that probability of odd numbers = 2 × (Probability of even number) ⇒ P (Odd) = 2 × P (Even) Now, P (Odd) + P (Even) = 1 ⇒ 2 P (Even) + P (Even) = 1 ⇒ 3 P (Even) = 1 P (Even) = 1/3 So, Now, Total number occurs on a single roll of die = 6 And the number greater than 3 = 4, 5 or 6 So, P (G) = P (number greater than 3) = P (number is 4, 5 or 6) Here, 4 and 6 are even numbers and 5 is odd ∴ P (G) = 2 × P (Even) × P (Odd) = 2 × 1/3 × 2/3 = 4/9 Hence, the required probability is 4/9