90% of flights depart on time. 80% of flights arrive on time. 75% of flights depart on time and arrive on time. Are the events, departing on time and arriving on time, independent?

Complete Question

90% of flights depart on time. 80% of flights arrive on time. 75% of flights depart on time and arrive on time.

• You are meeting a flight that departed on time. What is the probability that it will arrive on time?

• You have met a flight, and it arrived on time. What is the probability that it departed on time?

• Are the events, departing on time and arriving on time, independent?

1st Question

2nd  Question

3rd Question

      The probabilities are not independent

Step-by-step explanation:

From the question we are told that

    The  probability of flight that depart on time is  P(DT) = 0.9

      The probability of flights that arrive  on time  is  

     The  probability of flight that depart on time and arrive on time is  

    In the first question the flight is departed on time  so the probability that it will arrive on time is  

substituting values

In the second question the flight arrived on time, so the probability that it departed on time is  mathematically evaluated as follows

substituting values

Looking at the given and calculated values we see that the probability of  depart on time and arrive is not equal to the probability of  depart on time,

    i.e 0.75 =  0.8

the probability of  depart on time and arrive, and  the probability of depart on time are not independent

-2 is the right

step-by-step explanation: