Final answer:
The value of ‘p’, which represents the probability of event B, when A and B are independent events, is 1/3 or approximately 0.333.
Step-by-step explanation:
To find the value of ‘p’ when A and B are independent events, we use the formula for the probability of the union of two independent events, which is:
P(A ∪ B) = P(A) + P(B) - P(A and B)
Given that:
- P(A) = 0.4
- P(B) = p
- P(A ∪ B) = 0.6
For independent events A and B, the probability of A and B occurring together, denoted P(A and B), is equal to P(A) × P(B).
Therefore, P(A and B) = P(A) × P(B) = 0.4 × p.
Substituting the values into the union formula we get:
0.6 = 0.4 + p - (0.4 × p)
Solving for ‘p’ we have:
0.6 = 0.4 + p - 0.4p
0.6 - 0.4 = p - 0.4p
0.2 = 0.6p
p = 0.2 / 0.6
p = 1/3 or approximately 0.333