If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on time given that it was and Upstate Airlines flight.
_____________On Time Flights _________________ Late Flights
Podunk ___________ 33 ___________________________ 6
Upstate____________43 ___________________________ 5
To find the probability that a randomly selected flight, which is an Upstate Airlines flight, arrived on time, we need to divide the number of on-time Upstate Airlines flights by the total number of Upstate Airlines flights.
From the given information, we know that there are 43 on-time Upstate Airlines flights out of a total of 87 flights.
Therefore, the probability can be calculated as:
Probability = Number of on-time Upstate Airlines flights / Total number of Upstate Airlines flights
Probability = 43 / 87
Probability ≈ 0.494
So, the probability that a randomly selected flight, which is an Upstate Airlines flight, arrived on time is approximately 0.494 or 49.4%.
To find the probability that the selected flight arrived on time given that it was an Upstate Airlines flight, we need to use conditional probability.
Conditional probability is calculated by dividing the number of favorable outcomes (in this case, the number of on-time flights from Upstate Airlines) by the number of total outcomes (the total number of flights from Upstate Airlines).
In this case, there were 43 flights from Upstate Airlines, of which 43-5=38 were on time. So, the numerator (number of favorable outcomes) is 38.
The denominator (number of total outcomes) is the total number of flights from Upstate Airlines, which is 43.
Therefore, the probability that the selected flight arrived on time given that it was an Upstate Airlines flight is 38/43.
Are you studying Markov's chains?
let's set up a transition matrix
33/87 6/87
43/87 5/87
let's multiply [0 1] by this matrix to get
[ 43/87 5/87]
(first number represents ontime-Upstate)
so how about 43/87 or .4943 ?
Not absolutely sure about this.