Question

On a certain airline’s Atlanta to Chicago route, the chance that the early flight is full is 0.8. The chance that the late flight is full is 0.7. The chance that both flights are full is 0.6. Can we believe that the two flights being full are independent events? yes We do not have enough information to determine the answer. no

Answer 1

Answer:

No, we can't believe that the two flights being full are independent events.

Step-by-step explanation:

We are given that On a certain airline’s Atlanta to Chicago route, the chance that the early flight is full is 0.8. The chance that the late flight is full is 0.7. The chance that both flights are full is 0.6.

Let Probability that the early flight is full = P(E) = 0.8

Probability that the late flight is full = P(L) = 0.7

Probability that both flights are full = $P(E \bigcap L)$ = 0.6

Now, it is stated that for any two events to be considered as independent events following condition must gets fulfilled, i.e.;

Suppose there are two events A and B, so for these two events to be independent;

                  $P(A) \times P(B) = P(A \bigcap B)$

So, according to our question;

                  $P(E) \times P(L) = P(E \bigcap L)$  ----- for these events to be independent

                  $0.8 \times 0.7 \neq 0.6$

                        $0.56 \neq 0.60$

Since, the required condition is not fulfilled so we can't believe that the two flights being full are independent events.