At certain times of the year, about 70% of airline flight delays are caused by bad weather. During those times, about 50% of all flights experience bad weather, and about 25% of all flights are delayed.

Given these percentages, if the weather is good, what is the probability that your flight will be delayed?

About 35%

About 20%

About 15%

About 30%
Show your work.

About 15%

Step-by-step explanation:

Good weather: G

Bad weather: B

Delayed: D

P(B) = 0.5

P(G) = 1 - 0.5 = 0.5

P(B & D) + P(G & D) = P(D)

(0.7 × 0.25) + P(G & D) = 0.25

P(G & D) = 0.075

P(D/G) = P(G & D)/P(G)

= 0.075/0.5

= 0.15 × 100

= 15%

C

Step-by-step explanation:

Let's say that we have 1000 flights, just to make it simple. Then since 25% of all flights are delayed, that's about 25/100 * 1000 = 250 flights delayed. We also know that 70% of these 250 flights are delayed by bad weather, which would be 70/100 * 250 = 175 flights delayed by bad weather.

This means that 250 - 175 = 75 flights are delayed, not by bad weather; in other words, these are flights delayed in good weather.

Finally, since 50% of all flights experience bad weather, then 100% - 50% = 50% experience good weather: 50% * 1000 = 500.

Divide 75 by 500: (75/500) * 100 = 15%.

The answer is C.