If P(A/B)=1 must A=B?
The question also asks for a Venn diagram to explain the answer.
To equal 1, both numerator and denominator need to be the same value.
Cannot do Venn diagram here.
To determine whether P(A/B) = 1 implies that A = B, we need to understand what the notation P(A/B) means. P(A/B) denotes the conditional probability of event A given that event B has already occurred.
If P(A/B) = 1, it means that event A is certain to occur given that event B has occurred. In other words, event A and event B are strongly dependent on each other.
However, it does not necessarily mean that A is equal to B. The events A and B can be different, but they have a conditional probability of 1, which indicates a strong relationship between the two events.
To illustrate this, consider an example: Let A be the event of rolling a 6-sided fair die and getting an even number, and B be the event of getting an even number.
P(A/B) = 1 because if event B occurs (getting an even number), event A (getting an even number on a fair 6-sided die) is guaranteed to occur. However, A and B are not the same events; B is a subset of A. In this case, A consists of the set {2, 4, 6}, while B consists of the set {2, 4, 6} as well.
Therefore, P(A/B) = 1 does not imply that A = B, but it indicates a strong relationship between the two events.