80% of an airline's flights depart on-time and 20% do not. Of those that depart on-time, 95% arrive on-time. OF those that depart late, 10% arrive on-time. What is the chance of someone taking a flight that will arrive on-time?
0.78
Well, it seems like this airline has quite the sense of humor when it comes to punctuality! Let's break it down.
First, we need to find the probability of departing on-time and arriving on-time. We know that 80% of flights depart on-time, and out of those, 95% arrive on-time. So, the probability of departing on-time and arriving on-time is 80% multiplied by 95%, which is 76%.
Next, we need to find the probability of departing late and arriving on-time. We know that 20% of flights depart late, and out of those, 10% arrive on-time. So, the probability of departing late and arriving on-time is 20% multiplied by 10%, which is 2%.
Now, we just add up the probabilities of departing on-time and arriving on-time, and departing late and arriving on-time. So, the chance of someone taking a flight that will arrive on-time is 76% + 2%, which is 78%.
So, there you have it! The chance of someone taking a flight that will arrive on-time is 78%. Let's hope this airline's flights aren't as "late" as their sense of humor!
To find the chance of someone taking a flight that will arrive on-time, we can use a conditional probability approach.
Let's break it down into steps:
Step 1: Calculate the probability of a flight departing on-time.
Given that 80% of flights depart on-time, the probability of a flight departing on-time is 0.8 or 80%.
Step 2: Calculate the probability of a flight departing late.
Given that 20% of flights do not depart on-time, the probability of a flight departing late is 0.2 or 20%.
Step 3: Calculate the probability of a flight departing on-time and arriving on-time.
Given that 95% of flights that depart on-time arrive on-time, the probability of a flight departing on-time and arriving on-time is 0.8 * 0.95 = 0.76 or 76%.
Step 4: Calculate the probability of a flight departing late and arriving on-time.
Given that 10% of flights that depart late arrive on-time, the probability of a flight departing late and arriving on-time is 0.2 * 0.10 = 0.02 or 2%.
Step 5: Calculate the overall probability of a flight arriving on-time.
To calculate the overall probability of a flight arriving on-time, we need to consider both the probability of a flight departing on-time and arriving on-time, as well as the probability of a flight departing late and arriving on-time.
Overall probability = (probability of departing on-time and arriving on-time) + (probability of departing late and arriving on-time)
= 0.76 + 0.02
= 0.78 or 78%
Therefore, the chance of someone taking a flight that will arrive on-time is 78%.
To find the chance of someone taking a flight that will arrive on-time, we need to consider two scenarios: (1) when the flight departs on-time, and (2) when the flight departs late.
Scenario 1: When the flight departs on-time:
From the given information, we know that 80% of the airline's flights depart on-time, and of those that depart on-time, 95% arrive on-time. Using these percentages, we can calculate the probability of someone taking a flight that departs on-time and arrives on-time as follows:
(80% of flights depart on-time) * (95% of on-time departures arrive on-time)
= 0.80 * 0.95
= 0.76 or 76%
Scenario 2: When the flight departs late:
From the given information, we know that 20% of the airline's flights do not depart on-time, and of those that depart late, 10% arrive on-time. Using these percentages, we can calculate the probability of someone taking a flight that departs late and arrives on-time as follows:
(20% of flights depart late) * (10% of late departures arrive on-time)
= 0.20 * 0.10
= 0.02 or 2%
To find the overall chance of someone taking a flight that will arrive on-time, we can sum up the probabilities from both scenarios:
Probability of on-time departure and arrival + Probability of late departure and on-time arrival
= 76% + 2%
= 78%
Therefore, the chance of someone taking a flight that will arrive on-time is 78%.
arriving on time:
Pr= (.8*.95+.2*.1)=
calculate that, less than 80 percent