Question

The probability that there will be an accident on highway 17 each day depends on the weather. if the weather is dry that day, there is a 0.2% chance of an accident on highway 48; if the weather is wet that day, there is a 1.0% chance of an accident. today, the weather station announced that there is a 20% chance of the weather being wet. what is the probability that there will be an accident on highway 17 today?

Answer 1

.0036

Explanation:

Probability of accident and wet today is .2 times .01 which is .002.

Probability of accident and dry today is .8 times .002 which is .0016

Add those two numbers together to get .0036.

Answer 2

0.0036

Explanation:

The probabilities that the weather today will be

• wet -
  `Pr(\text{weather is wet})=0.2;`
• dry -
  `Pr(\text{weather is dry})=1-0.2=0.8.`

If the weather is wet, then the probabilities that the accident

• will occur -
  `Pr(\text{accident will occur})=0.01;`
• will not occur -
  `Pr(\text{accident will not occur})=1-0.01=0.99.`

If the weather is dry, then the probabilities that the accident

• will occur -
  `Pr(\text{accident will occur})=0.002;`
• will not occur -
  `Pr(\text{accident will not occur})=1-0.002=0.998.`

If the weather station announced that there is a 20% chance of the weather being wet, the probability that there will be an accident on highway 17 today is

`Pr=Pr(\text{weather is wet})\cdot Pr(\text{accident will occur})+Pr(\text{weather is dry})\cdot Pr(\text{accident will occur})=0.2\cdot 0.01+0.8\cdot 0.002=0.002+0.0016=0.0036.`