To understand the relationship between two events A and B given their probabilities, we can use the basic principles of probability.
We know that:
- P(A) = 0.7
- P(B) = 0.4
- P(A ∩ B) = 0.2
Now, let’s break down what these probabilities mean:
– P(A) is the probability that event A occurs, which is 70%.
– P(B) is the probability that event B occurs, which is 40%.
– P(A ∩ B) is the probability that both events A and B occur at the same time, which is 20%.
Using this information, we can calculate a few more probabilities:
- P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Substituting in our values:
P(A ∪ B) = 0.7 + 0.4 – 0.2 = 0.9
This means there is a 90% chance that either event A or event B occurs or both occur. This shows that events A and B are not mutually exclusive since P(A ∩ B) is greater than zero.
In conclusion, knowing the probabilities of events A and B allows us to deduce their relationship and calculate their union. This can be useful in various applications such as risk assessment, decision-making, and statistical analysis.