Mathematics, 03.02.2020 22:55 rockinrachel9099

For flights from a particular airport in january, there is a 30 percent chance of a flight being delayed because of icy weather. if a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. if a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. if one flight is selected at random from the airport in january, what is the probability that the flight selected will have at least one of the two types of delays?

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Answer from: katelynbychurch

The probability that the flight selected will have at least one of the two types of delays is 0.335 .

1. There is a % chance of a flight being delayed because of icy weather, $\therefore$ probability of being delayed is P(a)=0.3

probability of not being delayed is P(a')=1-0.3=0.7 .

2. If a flight is delayed because of icy weather, there is % chance the flight will also be delayed because of a mechanical problem,

$\therefore$ probability of being delayed is P(b)=0.1

probability of not being delayed is P(b')=1-0.1=0.9 .

3. If a flight is not delayed because of icy weather, there is % chance that it will be delayed because of a mechanical problem ,

$\therefore$ probability of being delayed is P(c)=0.05

probability of not being delayed is P(c')=1-0.05=0.95 .

Delayed of mechanical problem when weather is not icy is:

$P(a'\cap c)=P(a').P(c)=0.7\times 0.05=0.035$

Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is

$P(a'\cap c)+P(a)=0.035+0.3=0.335$

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For flights from a particular airport in january, there is a 30 percent chance of a flight being del

Answer from: Hernandezx9824

0.335

Step-by-step explanation:

1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.

2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.

3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)

Delayed of icy weather - 0.3

Delayed of MP when weather is not icy - 0.7·0.05=0.035

Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is

0.3+0.035=0.335

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

step-by-step explanation:

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