In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is

Step-by-step solution

The sample space for a fair die toss is S = 1, 2, 3, 4, 5, 6 with n(S) = 6 total outcomes. Let E represent the event that a 4 or 5 appears, so E = 4, 5 with n(E) = 2 favorable outcomes. The probability is P(E) = n(E) n(S) = 2 6 = 1 3 . The odds against E are expressed as P(E') : P(E) , where E' denotes the complement of E . The complement consists of outcomes 1, 2, 3, 6 , so P(E') = 4 6 = 2 3 . The odds ratio becomes 2 3 : 1 3 , which simplifies to 2 : 1 after multiplying both terms by 3. Odds against the event: A