Identify why this assigbment if probabilities cannot be legitimite: P(A)=0.4, P(B)=0.3, P(AandB)= 0.5
Dont know what you're trying to say from "Identify why this assigbment if probabilities cannot be legitimite"...
by P(AandB) do you mean P(A intercept B) or P(A union B)?
The probability of both/all events occurring is found by multiplying the probabilities of the individual events.
.4 * .3 ≠ .5
The probabilities provided in the assignment seem to be conflicting and therefore cannot be legitimate. Let's analyze each probability and see why they do not align.
1. Probability of A (P(A)) = 0.4: This indicates that the probability of event A occurring is 0.4 or 40%. This probability is acceptable.
2. Probability of B (P(B)) = 0.3: This indicates that the probability of event B occurring is 0.3 or 30%. This probability is also acceptable.
Now, let's consider the joint probability of A and B (P(A and B)) = 0.5. The joint probability represents the probability of both events A and B occurring simultaneously.
However, there is an issue here. According to the given probabilities, the joint probability (P(A and B)) is greater than the individual probabilities of A (P(A)) and B (P(B)). This contradicts the fundamental principle of probability, which states that the joint probability cannot be greater than the individual probabilities of the events.
In other words, it is not possible for both events A and B to occur with a probability of 0.5 when the individual probabilities of A and B are 0.4 and 0.3, respectively.
Therefore, the assignment of probabilities provided (P(A) = 0.4, P(B) = 0.3, P(A and B) = 0.5) cannot be legitimate and might need correction or clarification.