# Probability that the driver is from G3

• 2RIP
In summary: The notation you are using is more suited for advanced probability thinking, and the answer is not in a form that is easily understandable. Thanks for trying, but this is not an answer.
2RIP
There are three groups of drivers in a city: G1, G2, and G3.

G1 make up 30% of drivers, G2 make up 50% of drivers, and G3 make up the remaining 20% of drivers.

P(at least one accident for G1)=0.1 = P(A1)
P(at least one accident for G2)=0.3 = P(A2)
P(at least one accident for G3)=0.5 = P(A3)

If we randomly select a driver out of the groups and the driver has no accident, what is probability that the driver is from G3?

I tried $$P(G3 | (A1^{c} \cap A2^{c} \cap A3^{c}))$$. Is this is the right method of solving such a question? The probability I got from this happened to be zero which sort of confirms that it's incorrect. Any advice will be great.

Thanks a lot.

2RIP said:
There are three groups of drivers in a city: G1, G2, and G3.

G1 make up 30% of drivers, G2 make up 50% of drivers, and G3 make up the remaining 20% of drivers.

P(at least one accident for G1)=0.1 = P(A1)
P(at least one accident for G2)=0.3 = P(A2)
P(at least one accident for G3)=0.5 = P(A3)

If we randomly select a driver out of the groups and the driver has no accident, what is probability that the driver is from G3?

I tried $$P(G3 | (A1^{c} \cap A2^{c} \cap A3^{c}))$$. Is this is the right method of solving such a question? The probability I got from this happened to be zero which sort of confirms that it's incorrect. Any advice will be great.

Thanks a lot.

I like the brute force way since I don't know the notation. Assuming one hundred drivers in proportions given, 30 G1 drivers, etc. 1- prob of one accident is prob of no accidents, right ? So there are 27 no accident G1 drivers. Add up all the no accident drivers for G2 and G3, should be 72. What proportion of these 72 are G3 ? Well, there are 10 no accident G3 drivers, so 10/72 is probability.

It would be nice if the answer could be put in a form more in line with advanced probability thinking. So...?

For conditional probability: $$P(A\mid B)=\frac{P(A and B)}{P(B)}$$

So in this case A represents G3 and B represents no accident.

$$\frac{20*.5}{30*.9+50*.7+20*.5} = 10/27$$

I would not say that this "improves" the answer whatsoever, or even whether it applies.

Last edited:

## 1. What is the probability that the driver is from G3?

The probability that the driver is from G3 can be calculated by dividing the number of drivers from G3 by the total number of drivers. This is known as the probability of an event and is expressed as a decimal or percentage.

## 2. How is the probability of the driver being from G3 calculated?

The probability of the driver being from G3 is calculated by dividing the number of drivers from G3 by the total number of drivers. This is known as the probability of an event and is expressed as a decimal or percentage.

## 3. What factors influence the probability of the driver being from G3?

The probability of the driver being from G3 can be influenced by various factors such as the total number of drivers, the number of drivers from G3, and the characteristics of the drivers from G3 (e.g. age, gender, etc.). Other external factors, such as location and time, may also play a role in determining the probability.

## 4. Is the probability of the driver being from G3 the same for all drivers?

No, the probability of the driver being from G3 may vary for different groups of drivers. Factors such as demographics, driving patterns, and location can affect the likelihood of a driver being from G3. It is important to consider these factors when calculating probabilities.

## 5. How can the probability of the driver being from G3 be used in research or real-life situations?

The probability of the driver being from G3 can be used in various ways, such as predicting the likelihood of a driver being from G3 in a certain location or time period. It can also be used in research to compare different groups of drivers and their likelihood of being from G3. In real-life situations, this probability can be used to inform decision-making processes, such as targeting marketing campaigns or implementing safety measures for a specific group of drivers.

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