Suppose that the probability of winning the lottery, event A, is 1 in 10 million and the probability of experiencing an airplane crash , event B is 2.5 in 1 million. 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 time 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 time 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 P(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 than a lottery ticket
P(A) =0.500
P(B) =0.200
P(A and B) = 0.100
Are events A and B independent?
TRUE
False