Traffic Fatalities
In 2016, there were 34,439 traffic fa...

Question

Traffic Fatalities

In 2016, there were 34,439 traffic fatalities in the United States, with 9,477 of them being alcohol related.

d. What is the probability that neither of two randomly selected traffic fatalities in 2016 were alcohol related?

Accepted Answer

Welcome back, everyone. In a certain year, 28,500 workplace injuries were reported in a country with 7200 of them resulting from machinery accidents. What is the probability that neither of the two randomly selected workplace injuries from that year resulted from machinery accidents? A 0.486. B. 0.559 C. 0.724 and D 0.592. So for this problem, we want to identify the probability that neither of the two randomly selected workplace injuries from that year resulted from machinery accidents. Now, what do we know? Well, essentially, the total number of workplace injuries is 28,500. And 7200 of them resulted from machinery accidents. Now, if we subtract these two numbers, we're going to get 21,300, and those will be non-machinery related injuries. Now, we want to identify the probability of two randomly selected workplace injuries. That resulted from machinery accidents. So we're going to use the multiplication rule for dependent events. Let's remember the formula. The probability that A and B occur is equal to the probability of a. Multiplied by the probability of B given that a occurred. So now let's remember the formula for probability. Specifically, initially we're choosing our first. Event right and that would be. A random selection. Among all of those injuries, specifically, we want to divide the total number of favorable outcomes by The number of possible outcomes. Now the favorable outcomes for an event A, meaning choosing a non-machinery related injury would be 21,300, so that's our numerator, and our denominator would be the total number of total number of injuries reported, which is 28,500. So this is the probability to randomly select. An injury that is non-machinery related. Now for the second probability of B, given that A occurred, our numerator essentially decreases by 1 unit since we have already selected one of those injuries. So now the numerator is going to be 21,299. And our denominator is going to decrease by one unit as well because the total number of the remaining injuries reported. Decreases by 1 since we have already selected one of those injuries, so we get 28,499. And now what we want to do is multiply these two numbers. Using a calculator, we are going to get 0.55. 9 which corresponds to the answer choice B. Thank you for watching.

Traffic Fatalities
In 2016, there were 34,439 traffic fatalities in the United States, with 9,477 of them being alcohol related.
d. What is the probability that neither of two randomly selected traffic fatalities in 2016 were alcohol related?

Key Concepts

Probability of an Event

Complement Rule

Multiplication Rule for Independent Events

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Traffic FatalitiesIn 2016, there were 34,439 traffic fatalities in the United States, with 9,477 of them being alcohol related.d. What is the probability that neither of two randomly selected traffic fatalities in 2016 were alcohol related?