Consider two events such that P (A) = start fraction one over four end fraction, P (B) = start fraction two over five end fraction, and P (A ∩ B) = start fraction one over 10 end fraction full stop. Are events A and B independent events?

Question

Mathematics

Guest

11 December, 15:54

Consider two events such that P (A) = start fraction one over four end fraction, P (B) = start fraction two over five end fraction, and P (A ∩ B) = start fraction one over 10 end fraction full stop. Are events A and B independent events?

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Answers (1)

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Frank Key · Answer 1

Yes they are independent events

Step-by-step explanation:

In order to solve this, you need to first know the definition of probability of independent event.

two events are independent if the incidence of one event does not affect the probability of the other event. When that occurs, the expression or formula to calculate is the following:

P (A∩B) = P (A) * P (B)

So, in order to see if A and B are independent, let's see how the calculations do with the data provided

P (A∩B) = P (A) * P (B) = 1/4 * 2/5 = 2/20 = 1/10

Therefore, A and B are independent events