If events A and B are such that they are independent and p (a) = 0.3 and p(b) = 0.5
Find p (a n b) and p (a u b)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Either-or probabilities are found by adding the individual probabilities.
To find the probability of the intersection (A ∩ B) of events A and B, you can multiply their individual probabilities: p(A ∩ B) = p(A) * p(B).
Here, p(A) = 0.3 and p(B) = 0.5. So, p(A ∩ B) = 0.3 * 0.5 = 0.15. Therefore, the probability of event A and event B both occurring is 0.15.
To find the probability of the union (A ∪ B) of events A and B, you can use the formula: p(A ∪ B) = p(A) + p(B) - p(A ∩ B).
Using the given values, p(A ∪ B) = 0.3 + 0.5 - 0.15 = 0.65. Therefore, the probability of either event A or event B (or both) occurring is 0.65.
To summarize:
- The probability of A and B both occurring (A ∩ B) is 0.15.
- The probability of either A or B (or both) occurring (A ∪ B) is 0.65.