Question

Im confused on differences in binomial probabilties between x=0 x>6 and x<6. If somebody could explain how what each answer means in terms of searching for the answer in the table, such as in x<6 you subtract by one and why it would be greatly appreciated. Just to clarify i need somebody to explain what x=6 x>6 and x<6 means in terms of searching for the answer in the chart and why,

Answer 1

P(X = 0) implies the probability of occurrence of no events.

P(X = 6) implies the probability of occurrence of 6 events.

P(X > 6) implies the probability of occurrence of more than 6 events. We can put it alternatively as P(X 7), which implies occurrence of at least 7 events.

P(X < 6) implies the probability of occurrence of less than 6 events. We can put it alternatively as P(X 5), which implies occurrence of at most 5 events.

Also, we know, P(X > 6) + P(X 6) = 1 i.e. P(X > 6) + P(X = 6) + P(X < 6) = 1 i.e. P(X > 6) = 1 - P(X = 6) - P(X < 6).