Question

Given p(a)=0.40, p(b)=0.50. if a and b are independent, what is the value of p(a intersection b)?

Answer 1

Draw a Venn diagram to better understand. However:

P(A) = 0.4
P(B) =0.5
We have to calculate their intersection P(A∩B). This is a conditional probability, then

P(A∩B) = P(A) x P(B) = 0.4 x 0.5. So P(A∩B) = 0.2

Answer 2

Answer:  The required value is P(A intersection B) = 0.20.

Step-by-step explanation:  Given that for two independent events A and B,

P(A) = 0.40  and  P(B) = 0.50.

We are to find the value of $P(A\cap B).$

For any two independent events, the probability of their intersection is equal to the product of their probabilities.

Since A and B are independent events, so we have

$P(A\cap B)=P(A)\times P(B)=0.40\times 0.50=0.20.$

Thus, the required probability of the intersection of A and B is 0.20.

That is, P(A intersection B) = 0.20.