Answer to Question #199694 in Statistics and Probability for kauser

Question

Three airlines is providing services in Rajkot, a city in Gujarat. Airline

‘Saras’ has 50% of all the scheduled flights, airline ‘Yug’ has 30%, and airline

‘Pushpak’ has the remaining 20%. Their on-time rates are 80%, 65%, and 40%,

respectively.

A plane has just left on time from Rajkot Airport. What is the probability that it will

reach to its destination on time?

Note: It is mandatory to Prepare Probability Tree Diagram

Answer 1

Given $P(S)=0.5, P(Y)=0.3, P(P)=0.2,$

$P(Yes|S)=0.8, P(Yes|Y)=0.65, P(Yes|P)=0.4$

The Law of Total Probability

$$P(Yes)=P(S)P(Yes|S)+P(Y)P(Yes|Y)+P(P)P(Yes|P)$$

$$=0.5(0.8)+0.3(0.65)+0.2(0.4)$$

$$=0.4+0.195+0.08=0.675$$

The probability that it will reach to its destination on time is $0.675.$