# Calculating % of Drivers Who Died and Were Not Wearing Seatbelts

• kthouz
In summary, the conversation is about using Baye's Theorem to calculate the percentage of drivers who died and were not wearing seatbelts. The problem is solved using the formula of conditional probability, taking into account the percentages of drivers who wear seatbelts and those who die in accidents while wearing or not wearing seatbelts. The conversation also includes some clarifications and explanations of how to express certain probabilities in words.
kthouz
Hi! I have some problem about the use of Baye’s Theorem . So I have been given the problem below that we were asked to use Baye’s Theorem. But I sue the simple manner of conditional probability. So can somebody show me how I can use that Baye’s theorem or if I’m wrong correct me:
95% of car drivers wear seatbelt, 64% of car drivers involved in serious accident die if not wearing seatbelt whereas 12% of those that do wear a seatbelt die. Calculate, correct to 3 significant figures, the percentage of drivers who died and were not wearing seatbelts.
Let A= “wear seatbelt”; B= die; A’= don’t wear seatbelt.
P(A)= 95%
P(A’)=100%-95%=5%
P(B/A’)=64%
P(B and A’)=?
By formula of conditional probability P(B/A’)= [P(B and A’)]/[P(A’)]
Then P(B and A’)= [P(B/A’)]*[P(A’)]
P(B and A’)= 0.64*0.05=0.032=3.20%

We know that P(A) = .95, thus P(A') = .05.
Now let B be the event that someone died, like you put. Then you have
P(B | A') = P(B and A')/P(A') = .64 Since 64% of the people that don't wear seats belts die. Thus for P(B and A') = (.05)(.64).

Now we want P(A' | B) = P(A' and B)/P(B). Well you have P(A' and B) already, so now you just need to find the probability that someone died, P(B). There are two things to take into consideration here. The people that died and were wearing their seatbelts and the other side of the coin, the people who died and were not wearing their seatbelts.

Hope this helps.

daveyinaz said:
Now we want P(A' | B) = P(A' and B)/P(B). Well you have P(A' and B) already, so now you just need to find the probability that someone died, P(B). There are two things to take into consideration here. The people that died and were wearing their seatbelts and the other side of the coin, the people who died and were not wearing their seatbelts.

Hope this helps.
We know that the drivers who died and were wearing seatbelt are 12% and there 5% who died and were not wearing seatbelt.

So we have
P(B)= P(A and B) + P(A' and B)= 12% + 5% = 17%
P(A'/B)=P(A' and B)/P(B)=(.05)/(.17)
Is it like this?
But here i don't understand why you have calculated again that P(A'/B)! if i try to express it in words you meant the probability of A' conditionned by B or again "the drivers who were not wearing seatbelt but who died before"? Just here can you explain me how we can express that P(A'/B)?

kthouz said:
We know that the drivers who died and were wearing seatbelt are 12% and there 5% who died and were not wearing seatbelt.

So we have
P(B)= P(A and B) + P(A' and B)= 12% + 5% = 17%

Wait, I already told you that P(A' and B) = (.05)(.64) So why do you say that it's 5% above.
Think of it this way...of the 5% of the people that don't wear seatbelts 64% of them die, that is P(A' and B).

Now, we look at P(A and B); of the 95% that wear seatbelts, only 12% of them die.

Is this more clear?

## 1. How is the percentage of drivers who died and were not wearing seatbelts calculated?

The percentage of drivers who died and were not wearing seatbelts is calculated by dividing the number of drivers who died while not wearing seatbelts by the total number of drivers who died in a given time period, and then multiplying by 100 to get the percentage.

## 2. Why is it important to calculate the percentage of drivers who died and were not wearing seatbelts?

Calculating this percentage helps to understand the impact of not wearing a seatbelt on the likelihood of death in a car accident. It also provides valuable information for promoting seatbelt use and implementing safety measures.

## 3. What data is needed to calculate the percentage of drivers who died and were not wearing seatbelts?

The data needed includes the total number of drivers who died and the number of those drivers who were not wearing seatbelts. This information can be obtained from traffic accident reports and statistics from government agencies.

## 4. How does the percentage of drivers who died and were not wearing seatbelts vary by age or gender?

The percentage of drivers who died and were not wearing seatbelts may vary by age or gender, as certain demographics may be more likely to wear seatbelts than others. This information can be further analyzed to target specific groups for education and awareness campaigns.

## 5. Can the percentage of drivers who died and were not wearing seatbelts be influenced by other factors?

Yes, the percentage of drivers who died and were not wearing seatbelts can be influenced by other factors such as road conditions, weather, and type of vehicle. It is important to consider these factors when interpreting the data and making conclusions about the effectiveness of seatbelt usage.

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