Question

On a certain airline, the chance the early flight from Atlanta to Chicago is full is 0.8. The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Can we believe the two flights being full are independent events?a) yesb) no

Answer 1

Correct option: b

Explanation:

Independent events are those events that can occur together at the same time. That is, they do not effect the occurrence of each other.

The joint probability of two independent events A and B is:

`P(A\cap B)=P(A)* P(B)`

Denote the events as follows:

X = the early flight from Atlanta to Chicago is full

Y = the late flight from Atlanta to Chicago is full

The information provided is:

P (X) = 0.80

P (Y) = 0.70

P (X ∩ Y) = 0.60

If events X and Y are independent then,

`P(X\cap Y)=P(X)* P(Y)`

Check whether the two events are independent or not as follows:

`P(X\cap Y)=P(X)* P(Y)\\=0.80*0.70\\=0.56\\\\eq 0.60`

The events X and Y are not independent.

Thus, the events of a early flight being full and a late flight being full are not independent.