At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.17 and the probability that the flight will be delayed is 0.16. The probability that it will rain and the flight will be delayed is 0.07. What is the probability that it is not raining and the flight leaves on time? Round your answer to the nearest thousandth.

100 - (Probability for raining + Probability for fight delay + Probability for Raining and fligth delay ) = Probability for no rain and flight on time.

So, 100-(0.17+0.16+0.07) = Probability for no rain and flight on time.

100-(0.40) = Probability for no rain and flight on time.

99.60=Probability for no rain and flight on time.

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Yogeshkumari Yogeshkumari · Answer 2 · 2022-05-17T18:06:55+02:00

Probability of not raining and flight leaves on time is equals to 0.740.

What is Probability?

" Probability is defined as a branch of mathematics which represents ratio number of favourable to the total number of outcomes."

Formula used

De Morgan's law

P( A'∩ B') = P (A∪B)'

P (A∪B)' = 1 - P (A∪B)

P(A∪B) = P(A) + P(B) - P(A∩B)

According to the question,

Let Probability of rain = P(A)

= 0.17

Probability of flight delay =P(B)

= 0.16

Therefore ,

Probability of rain and flight delay = P (A∩B)

= 0.07

Probability of not raining and flight on time = P( A'∩ B')

Substitute the values in the formula

P( A'∩ B') = 1 - [ 0.17 + 0.16 -0.07]

= 1- 0.26

= 0.74

= 0.740 ( nearest thousandth)

Hence, Probability of not raining and flight leaves on time is equals to 0.740.

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