## 10. Auto Rally

This was an extremely dangerous auto rally. It started with a small and very narrow bridge, where one out of five cars fell into the water. Then came a terrible sharp turn, where three out of ten cars ended up in the ditch. Further along the way, there was such a dark and winding tunnel that one out of ten cars crashed in it. And the final stretch of the route was a sandy road, where two out of five cars got hopelessly stuck in the sand.

The task is to find the overall percentage of cars that were involved in accidents during the rally.
10. For a car to successfully complete an auto rally, it must not get into an accident on the bridge (which happens in 4 out of 5 cases), nor on a curve (7 out of 10), nor in a tunnel (9 out of 10), nor, finally, on a sandy road (3 out of 5). Thus, we get

$$
\frac{4 \cdot 7 \cdot 9 \cdot 3}{5 \cdot 10 \cdot 10 \cdot 5}=0.302
$$

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-106.jpg?height=896&width=1422&top_left_y=266&top_left_x=314)

Therefore, the percentage of cars that got into an accident during the auto rally is

$$
100-(100 \cdot 0.302) \approx 70 \%
$$