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Math

QuestionFind the probability P\mathrm{P} (checked bags | final destination) using the given passenger data.

Studdy Solution

STEP 1

Assumptions1. The total number of passengers who checked their bags and this is their final destination is64. . The total number of passengers who did not check their bags and this is their final destination is90.
3. The total number of passengers who checked their bags and this is not their final destination is30.
4. The total number of passengers who did not check their bags and this is not their final destination is16.
5. The passenger is chosen at random.

STEP 2

First, we need to find the total number of passengers who have reached their final destination. We can do this by adding the number of passengers who checked their bags and reached their final destination to the number of passengers who did not check their bags and reached their final destination.
Total final destination passengers=Checked bags final destination passengers+Did not check bags final destination passengersTotal\, final\, destination\, passengers = Checked\, bags\, final\, destination\, passengers + Did\, not\, check\, bags\, final\, destination\, passengers

STEP 3

Now, plug in the given values for the checked bags final destination passengers and did not check bags final destination passengers to calculate the total final destination passengers.
Total final destination passengers=64+90Total\, final\, destination\, passengers =64 +90

STEP 4

Calculate the total number of final destination passengers.
Total final destination passengers=64+90=154Total\, final\, destination\, passengers =64 +90 =154

STEP 5

Now that we have the total number of final destination passengers, we can find the probability of a passenger checking their bags given that this is their final destination. This is calculated by dividing the number of passengers who checked their bags and reached their final destination by the total number of final destination passengers.
(checked bags∣final destination)=Checked bags final destination passengersTotal final destination passengers(checked\, bags | final\, destination) = \frac{Checked\, bags\, final\, destination\, passengers}{Total\, final\, destination\, passengers}

STEP 6

Plug in the values for the checked bags final destination passengers and the total final destination passengers to calculate the probability.
(checked bags∣final destination)=64154(checked\, bags | final\, destination) = \frac{64}{154}

STEP 7

Calculate the probability.
(checked bags∣final destination)=64154≈0.4156(checked\, bags | final\, destination) = \frac{64}{154} \approx0.4156The probability that a passenger checked their bags given that this is their final destination is approximately0.4156.

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