Question

A car was involved in a hit and run accident, with Dewald there to witness it. It turns out that 1 in 10 cars on the road is a self-driving car. Dewald said the car involved was a self-driving car. The court tested Dewald’s reliability and concluded that he correctly identified what type of car he saw 80% of the time. What is the probability that the car involved in the accident was a self-driving car, given Dewald’s testimony? Please enter the answer in percentages to the nearest two decimals places: e.g. 50.00%

Answer 1

Answer:

25%

Step-by-step explanation:

The car being a self-driven car and Dewald's testimony both are independent events

Let T be an event

T : Dewald testified the car to be self-driven

Then P(T)

= Probability that the car was self driven and Dewald testified it correctly + Probability that the car was not self-driven and Dewald testified it incorrectly

$=0.1\times 0.8+0.9\times 0.2$

$=0.08+0.18$

$=0.36$

Let S be an event

S : The car was self-driving car

Then by Bayes' Theorem

$P(S/T)=\frac{P(S\cap T)}{P(T)}$

$\implies P(S/T)=\frac{0.1\times 0.8}{0.36}$

$\implies P(S/T)=\frac{8}{36}$

$\implies P(S/T)=\frac{1}{4}$

$\implies P(S/T)=0.25$

% that the car was a self driving car= 25%

Hope this helps.