Question

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?

Answer 1

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?

Answer:

1st Question

       $P(X_1) = 0.833$

2nd  Question

      $P(X_2) = 0.938$

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  $P(AT) = 0.8$

     The  probability of flight that depart on time and arrive on time is  $P(DT\ |\ AT) = 0.75$

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

         $P(X_1) = \frac{P(DT\ | \ AT)}{DT}$

substituting values

         $P(X_1) = \frac{0.75}{0.9}$

        $P(X_1) = 0.833$

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

           $P(X_2) = \frac{P(DT\ | \ AT)}{AT}$

substituting values

           $P(X_2) = \frac{0.75}{0.8}$

           $P(X_2) = 0.938$

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