Independent Sequential or Simultaneous Events An event which is independent does
ID: 3175892 • Letter: I
Question
Independent Sequential or Simultaneous Events An event which is independent does not affect the probability of occurrence of the next event. 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 determine the probability of winning the lottery and crashing on the way to a resort to enjoy your winnings. On average, of 10 trillion lifetimes, you won 10T times 1/10M = 1M lottery tickets. 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. So, P(AB) = 1/10M times 2.5/M. You should fly, but you may consider buying something other than the lottery ticket. The assumption of independence lead to P(A and B) = P(A) P(B). Conversely, if P(A and B) = P(A) x P(B), A and B are independent P(A) = 0.362 P(B) = 0.078 P(A and B) = 0 028 Are A and B independent events? Yes No How do you test independence?Explanation / Answer
21) Consider,
P(A).P(B) = 0.362*0.078
= 0.028
= P(A and B)
Therefore, A and B are independent.
22) When P(A and B) = P(A).P(B) then A and B are independent, otherwise they are dependent.