Question 1185738: The following table represents the age of drivers (in years) and the major causes of 944 car accidents.
Age Speeding Careless Drinking and Driving Total
Below 25 160 89 286 535
25 and above 136 219 54 409
Total 296 308 340 944
(a) Find the probability that a randomly chosen car accident is caused by a careless driver under 25 years old.
0.5667
(b) Find the probability that a randomly chosen car accident is caused by either drinking and driving or speeding.
(c) Find the probability that a randomly chosen car accident is caused by either drinking and driving or a driver under 25 years old.
(d) Given that a car accident was caused by speeding, calculate the probability that the driver was at least 25 years old.
(e) If two car accidents are randomly chosen (without replacement), calculate the probability that they are both caused by careless driving.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the breakdown of how to calculate the probabilities:
**(a) Probability of a careless driver under 25:**
* Number of accidents caused by careless drivers under 25: 89
* Total number of accidents: 944
* Probability = (Number of careless drivers under 25) / (Total accidents) = 89 / 944 ≈ 0.0943 (Your provided answer of 0.5667 is incorrect.)
**(b) Probability of drinking and driving OR speeding:**
* Number of accidents caused by drinking and driving: 340
* Number of accidents caused by speeding: 296
* Total accidents: 944
* Probability = (Drinking and driving + Speeding) / Total = (340 + 296) / 944 = 636 / 944 ≈ 0.6737
**(c) Probability of drinking and driving OR a driver under 25:**
* Number of accidents caused by drinking and driving: 340
* Number of accidents involving drivers under 25: 535
* Number of accidents caused by drinking and driving *and* a driver under 25: 286
* Probability = (Drinking and driving + Under 25 - Both) / Total = (340 + 535 - 286) / 944 = 589 / 944 ≈ 0.6239
**(d) Probability the driver was at least 25 GIVEN speeding:**
* Number of accidents caused by speeding: 296
* Number of accidents caused by speeding and a driver 25 or above: 136
* Probability = (Speeding and 25 or above) / (Total speeding) = 136 / 296 ≈ 0.4595
**(e) Probability of two careless driving accidents (without replacement):**
* Probability of the first accident being caused by careless driving: 308 / 944
* After one accident is chosen, there are 943 accidents left, and 307 are caused by careless driving.
* Probability of the second accident being caused by careless driving: 307 / 943
* Probability of both being caused by careless driving = (308 / 944) * (307 / 943) ≈ 0.1066
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