SOLUTION: A STUDY OF TRAFFIC PATTERNS IN A LARGE CITY SHOWS THAT IF THE WEATHER IS RAINY, THERE IS A 50% CHANCE OF AN ACCIDENT. IF THE WEATHER IS CLEAR THE CHANCE OF AN ACCIDENT IS REDUCED T

Question 1184900: A STUDY OF TRAFFIC PATTERNS IN A LARGE CITY SHOWS THAT IF THE WEATHER IS RAINY, THERE IS A 50% CHANCE OF AN ACCIDENT. IF THE WEATHER IS CLEAR THE CHANCE OF AN ACCIDENT IS REDUCED TO 25%. TOMORROWS WEATHER THERE IS A 75% CHANCE OF RAIN
WHAT IS THE PROBABILITY IT WILL RAIN TOMORROW ?
WHAT IS THE PROBABILITY THERE WILL BE AN ACCIDENT TOMORROW ?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Probability of rain tomorrow is 0.75
If it rains, the probability of an accident is 0.50, so that is overall 0.375 probability for that outcome.
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If it does not rain, with probability 0.25, there is 0.25 probability of an accident or 0.0625 probability for that outcome.
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Add the two, and the probability of an accident tomorrow is 0.4375.
Can do a rough check: if it rains, the probability of an accident is 0.50, but if no rain, which is part of the possibility tomorrow, then the probability is less, and that will bring down the overall probability, skewed closer to 0.50 than 0.25 since there is a higher probability it will rain than not rain.
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