Question

the probability that a flight arrives on time is 0.7 and the probability that a flight departs on time is 0.8.The probability that a flight neither arrives on time nor departs on time is 0.15. Then the probability that flight arrives on time and departs on time is?

Answer 1

Here given,

 probability that a flight arrives on time = P(A) = 0.7

probability that a flight departs on time = P(B) = 0.8.

probability that a flight neither arrives on time nor departs on time = P(A' $\bigcap$ B') = 0.15

probability that flight arrives on time and departs on time =P(A $\bigcap$ B)

Using De'morgan law P(A $\bigcup$ B)' = P(A' $\bigcap$ B')

so, P(A $\bigcup$ B)' = P(A' $\bigcap$ B') = 0.15

P(A $\bigcup$ B)' = 1- P(A $\bigcup$ B)

P(A $\bigcup$ B) = 1-P(A $\bigcup$ B)'

=1-0.15

=0.85

Now,

P(A $\bigcup$ B) = P(A) + P(B) -P(A $\bigcap$ B)

P(A $\bigcap$ B) = P(A) + P(B) - P(A $\bigcup$ B)

= 0.7 + 0.8 - 0.85

P(A $\bigcap$ B) = 0.65

ANSWER : probability that flight arrives on time and departs on time =P(A $\bigcap$ B)=0.65