Question

1. motor vehicle accidents during a recent year, there were 13.5 million automobile accidents, 5.2 million truck accidents, and 178,000 motorcycle accidents. if one accident is selected at random, find the probability that it is either a truck or motorcycle accident. what is the probability that it is not a truck accident? source: based on data from the national safety council.

Explanation:

Step1: Calculate total number of accidents

First, convert all values to the same unit (say, number of accidents). \(13.5\) million \( = 13500000\), \(178000=178000\), \(5.2\) million \(=5200000\).
Total number of accidents \(N=13500000 + 178000+5200000=18878000\)

Step2: Calculate probability of a truck accident

Let \(n_{truck}=178000\). Probability of a truck accident \(P(\text{truck})=\frac{n_{truck}}{N}=\frac{178000}{18878000}\)

Step3: Use the formula \(P(\text{not truck}) = 1 - P(\text{truck})\)

\(P(\text{not truck})=1-\frac{178000}{18878000}=\frac{18878000 - 178000}{18878000}=\frac{18700000}{18878000}=\frac{9350}{9439}\approx0.9906\)

Answer:

The probability that it is not a truck accident is \(\frac{9350}{9439}\approx0.9906\)