Event A is independent of event B if the occurrence of A does not affect the pro

Question

Event A is independent of event B if the occurrence of A does not affect the probability of occurrence of event B.

Suppose that the probability of winning the lottery, event A, is 1 in 10 million, and that the probability of experiencing an airplane crash, event B, is 2.5 in 1 million (I looked this up). These events are independent. You have been granted 10 trillion lifetimes to experience both winning the lottery and crashing on the way to a resort to not enjoy your winnings. On average, of 10 trillion lifetimes, you won 10T x 1/10M = 1M lotteries. On the accompanying flights, your plane crashes 2.5 times. So, the probability that you will win and crash is 2.5/10T. In general, P(A) of the time A occurs. P(B) of the time B occurs. When A and B share the same time, the events A and B coincide P (A) x P(B) of the time, or P (A and B) = P(A) x P(B), which is the simple multiplication rule. The assumption of independence leads to

-A and B are independent if P(A and B) = P(A) x (B)

-If P(A and B) = P(A) x P(B), A and B are independent.

Returning to the example, P(winning and crashing) = 1/10M x 2.5/M. You should fly, but you may consider buying something other than the lottery ticket.

P(A) = 0.500

P(B) = 0.200

P(A and B) = 0.100

Are events A and B independent?

True or False

Explanation / Answer

Correct Answer: True

since P(A) P(B) = 0.500*0.200 = 0.100 = P(A and B)

Therefore, A and B are Independent

Definition: Two events A and B are independent if P(A and B) = P(A) P(B)

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