Counterexample: A = event that an integer is less than 5 B = event that an integer is less than 10 Clearly P(A|B) = 1. The probability that the number isless than 5 is 100% if you are given that the number is less than10. The problem asks to show that P(Bc|Ac) = 1. But giventhat a number is not less than 5 (for example, 7) does not meanwith probability 100% that the number is not less than 10! Counterexample: A = event that an integer is less than 5 B = event that an integer is less than 10 Clearly P(A|B) = 1. The probability that the number isless than 5 is 100% if you are given that the number is less than10. The problem asks to show that P(Bc|Ac) = 1. But giventhat a number is not less than 5 (for example, 7) does not meanwith probability 100% that the number is not less than 10!
Explanation / Answer
A means less than5 You state " ClearlyP(A|B) = 1." This is not true. heprobability that the number is less than 5 is NOT 100% if you areONLY given that the number is less than 10. Oram I misunderstanding your question?