An airline tracks data on its flight arrivals. Over the past six months, 25 flights on one route arrived early, 150 arrived on time, 45 were late, and 30 were cancelled.

a. What is the probability that a flight is early? On time? Late? Cancelled?

b. Are these outcomes mutually exclusive?

c. What is the probability that a flight is either early or on time?

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windyyork windyyork · Answer 1 · 2019-08-12T12:06:16+02:00

Answer: a) 0.0625,0.375,0.1125,0.075 respectively.

b) Yes, they are mutually exclusive

c) 0.4375.

Step-by-step explanation:

Since we have given that

Number of flights on one route arrived early = 25

Number of flights arrived on time = 150

Number of flights were late = 45

Number of flights were cancelled = 30

Total number = 25+150+150+45+30 = 400

We need to find the probability that a flight is early is given by

[tex]\dfrac{25}{400}\\\\=0.0625[/tex]

Probability that a flight is on time is given by

[tex]\dfrac{150}{400}=0.375[/tex]

Probability that a flight is late is given by

[tex]\dfrac{45}{400}=0.1125[/tex]

Probability that a flight is cancelled is given by

[tex]\dfrac{30}{400}=0.075[/tex]

They are mutually exclusive as they have no dependence.

Probability that a flight is either early or on time is given by

[tex]\dfrac{25}{400}+\dfrac{150}{400}\\\\=\dfrac{175}{400}\\\\=0.4375[/tex]

Hence, a) 0.0625,0.375,0.1125,0.075 respectively.

b) Yes, they are mutually exclusive

c) 0.4375.