It is tempting to treat this like it is a Bernoulli experiment repeated 200 times resulting in a Binomial distribution as given below:

Answer:

$$1- (0.99)^{200} = 86.7\%$$

You are almost guaranteed of DEATH. Be careful about the risky things we do in life, including driving at high speed.

I disagree with this answer by Prof Arthur Mutambara on his **LinkedIn.** Here is my thinking.

1. The question requires the use of conditional problem given the way it is worded. Without loss of meaning, the same question can be written as follows:

**Given that it is a risky activity, the probability of death is $1\%$. If you carry out that activity 200 times, what is the probability of death?**

Using Bayes Theorem:

$$P(D|R) = \dfrac{P(R|D) \times P(D)}{P(R)}$$

Where

$P(D)$ is the probability of death each time (what we are trying to establish)

$P(R)$ is the risk rate (e.g. associated risk of being on the road)

$P(D|R)$ is the probability of death given that it was a risky activity

$P(R|D) is the risk given death

From the question $P(D|R) = 0.01$

From the **UNECA website** $P(R|D) =\dfrac{26.6}{100000}$ in Africa.

From intuition, $P(R)=0.99$ implying that the risk on the roads is high.

Substituting in Bayes Theorem:

$$0.01 = \dfrac{\dfrac{26.6}{100000} \times P(D)}{0.99}$$

Therefore $P(D) = 37.22\%$ everytime someone engages with the risky activity of travelling on some African road.

The 200 events are independent thus the only metric that matters is the probability of each individual outing.