Question

In a study of fatal car accidents, some accidents were attributed to high speed or drunk driving. a. The probability that the fatality was attributed to high speeds was 0.57. b. The probability that the fatality was attributed to drunk driving was 0.62. c. The probability that high speed and drunk driving caused the accident was 0.41. a. [2 pts] What is the probability that a fatal accident will be attributed to high speeds or drunk driving? b. [2 pts] What is the probability that a fatal accident will be attributed to neither cause? c. [2 pts] What is the probability that the fatality will be attributed to drunk driving, but not high speeds?

Answer 1

Answer:

a) Probability that a fatal accident will be attributed to high speeds or drunk driving is 0.37

b) Probability that a fatal accident will be attributed to neither cause is 0.22

c) Probability that the fatality will be attributed to drunk driving, but not high speeds is 0.21

Explanation:

The easiest way to solve this problem is to make a venn diagram to see the distribution of probability as it is in the image. For this you first need to establish the variables.

P(h) = Probability that a fatal accident will be attributed to high speeds

P(d) = Probability that a fatal accident will be attributed to drunk driving

P(hnd) = Probability that high speed and drunk driving caused the accident

P(hud) = Probability that a fatal accident will be attributed to high speeds or drunk driving

So we have the values for the following variables

P(h) = 0.57     P(d) = 0.62   P(hnd) = 0.41

1. In the diagram you can see that P(h) and P(d) include the probability of both so to calculate the probability  that a fatal accident will be attributed to high speeds or drunk driving we need to take out the intersection for each and add the result then:

P(hud) = (P(h) -  P(hnd)) + (P(d) - P(hnd)

P(hud) = (0.57 - 0.41) + (0.62 - 0.41)

P(hud) = 0.16 + 0.21

P(hud) = 0.37

So the probability that a fatal accident will be attributed to high speeds or drunk driving is 0.37

2. To calculate the probability that a fatal accident will be attributed to neither cause we need to substrat from the total probability that is 1 the probability of P(hud) with the probability of P(hnd) so we have all the information that is en each part of the diagram.

Probability of neither cause = 1.0 - (P(hud) + P(hnd))

Probability of neither cause = 1.0 - (0.37 + 0.41)

Probability of neither cause = 1.0 - 0.78

Probability of neither cause = 0.22

In the diagram it is what is out of the circles.

So the probability that a fatal accident will be attributed to neither cause is 0.22

3. To calculate the probability that the fatality will be attributed to drunk driving, but not high speeds we have to subtract to P(d), the probability of the intersection, P(hnd)

Probability just to drunk driving = P(d) - P(hnd)

Probability just to drunk driving = 0.62 - 0.41

Probability just to drunk driving = 0.21

In the diagram is what appears in the right of the red circle.

So the probability that the fatality will be attributed to drunk driving, but not high speeds is 0.21

Answer 2

Based on the data provided;

• probability of fatal accident due to high speed or drink driving is 0.37
• probability that the fatal accident is neither caused by high speed or drink driving is 0.22
• probability that the fatality will be attributed to drink driving, but not high speeds is 0.21

What is probability?

Probability is the likelihood or chance for a given event to occur or not.

• Probability = number of expected outcome/number of possible outcomes

From the given data of the study of fatal accidents;

Let S stand for fatalities from high speed and A for drink driving fatalities.

• P (S) = 0.57
• P (A) = 0.62
• Probability of S and A, P (SnA) = 0.41
• Probability of S or A, P (SuA) =

 

(a) P (SuA) = P (S) - P (SnA) + P (A) - P (SnA)

P (SuA) = 0.57 - 0.41 + 0.62 - 0.41

P (SuA) = 0.37

Thus, probability of fatal accident due to high speed or drink driving is 0.37

 

(b) Probability of neither cause = 'P (SuA)  

'P (SuA)  = 1 - P (SuA)

'P (SuA) = 1 - 0.78

'P (SuA) = 0.22

Thus, probability that the fatal accident is neither caused by high speed or drink driving is 0.22.

(c) Probability that the fatality will be attributed to drink driving, but not high speeds = P (A) - P ( SnA)

Probability due to just drink driving = 0.62 - 0.41

Probability due to just drink driving = 0.21

Thus, probability that the fatality will be attributed to drink driving, but not high speeds is 0.21

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