# The probability is 1 in 4,011,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 46,000 trips.(a) What is the probability of a

0.0114

Step-by-step explanation:

(a) What is the probability of a fatal accident over a lifetime?

Suppose A be the event of a fatal accident occurring in a single trip.

Given that:

P(1 single auto trip in the United States result in a fatality) = P(A)

Then;

P(A) = 1/4011000

P(A) = 2.493 × 10⁻⁷

Now;

P(1 single auto trip in the United States NOT resulting in a fatality) is:

P() = 1 -  P(A)

P() = 1 - 2.493 × 10⁻⁷

P() = 0.9999997507

However, P(fatal accident over a lifetime) = P(at least 1 fatal accident in lifetime i.e. 46000 trips)

= 1 - P(NO fatal accidents in 46000 trips)

Similarly,

P(No fatal accidents over a lifetime) = P(No fatal accident in the 46000 trips) = P(No fatality on the 1st trip and No fatality on the 2nd trip ... and no fatality on the 45999 trip and no fatality on the 46000 trip)

=

=

= 0.9885977032

Finally;

P(fatal accident over a lifetime) = 1 -  0.9885977032

P(fatal accident over a lifetime) = 0.0114022968

P(fatal accident over a lifetime) ≅ 0.0114

## Related Questions

-1 + 0 + 1 + ... + 12

77

Step-by-step explanation:

-1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 77

Hope this helps :)

A manufacturing company has two retail outlets. It is known that 40% of all potentialcustomers buy products from outlet 1 alone, 35% buy from outlet 2 alone, and 10% buy fromboth 1 and 2. LetAdenote the event that a potential customer, randomly chosen, buys fromoutlet 1, and letBdenote the event that the customer buys from outlet 2. Suppose a potentialcustomer is chosen at random. For each of the following events, represent the eventsymbolically and then find its probability.Required:
a. The customer buys from outlet 1.
b. The customer does not buy from outlet 2.
c. The customer does not buy from outlet 1 or does not buy from outlet 2.
d. The customer does not buy from outlet 1 and does not buy from outlet 2.

Step-by-step explanation:

Given

--- From outlet 1 alone

--- From outlet 2 alone

--- From both

Solving (a): Buys from outlet 1;

This is represented as: P(A)  and the solution is:

Solving (b): Does not buy from outlet 2;

This is represented as: P(B'):

First, calculate the probability that the customer buys from 2

Using the complement rule, we have:

Solving (c): Does not buy from 1 or does not buy from 2

This is represented as:

And the solution is:

Using complement rule:

The equation becomes:

Solving (d): Does not buy from 1 or does not buy from 2

This is represented as:

And it is calculated as:

A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and #8 are torqued correctly. State whether each of the following pairs of events is mutually exclusive.a. A and Bb. B and Dc. C and Dd. B and C

a

Mutually exclusive

b

Not Mutually exclusive

c

Not Mutually exclusive

d

Not Mutually exclusive

Step-by-step explanation:

From the question we are told that

The number of bolt is n = 12

The event that all the bolt are torqued correctly is A

The event that the 3rd bolt is not torqued correctly is B

The event that exactly one bolt is not torqued correctly is C

The event that the and are torqued correctly is D

Generally for an event to be mutually  exclusive it means that both event can not occur at the same time

Considering a

The  A and  B are mutually exclusive because they can not occur at the same time

Considering b

The  event B and D are not mutually exclusive because they can occur at the same time

Considering c

Event  C and  D are not mutually exclusive because they can occur at the same time

Considering d

Event       B and  C are not mutually exclusive because they can occur at the same time

Event pairs A and B, and B and C are mutually exclusive. Event pairs B and D and C and D are not mutually exclusive.

### Explanation:

In order to determine whether two events are mutually exclusive, we need to check if they can both occur at the same time. If the occurrence of one event necessarily means that the other event cannot occur, then the events are mutually exclusive. Let's analyze each pair of events:

a. A and B: These events are mutually exclusive because if all the bolts are torqued correctly (event A), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

b. B and D: These events are not mutually exclusive because it is possible for the #3 bolt to be not torqued correctly (event B) while the bolts #5 and #8 are torqued correctly (event D).

c. C and D: These events are not mutually exclusive because it is possible for exactly one bolt to not be torqued correctly (event C) while the bolts #5 and #8 are torqued correctly (event D).

d. B and C: These events are mutually exclusive because if exactly one bolt is not torqued correctly (event C), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

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If x=2 find y 5x-y=5

y=5

solution,

X=2

now,

hopethishelps..

33.7 rounded to the nearest ten

I think the answer is 30.
the anwser is 34 because 5 and up would round up

A direct mailing company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid. A recently taken random sample of 150 orders showed that 129 of them were mailed within 72 hours. Set up the null and alternative hypotheses to test whether the company’s claim is true?

The null and alternative hypothesis are:

There is not enough evidence to support the claim that the company is worng and less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The company's claim is the null hypothesis, the claim that is going to be tested is if this proportion is significantly less than 90%.

Then, the null and alternative hypothesis are:

The significance level is 0.05.

The sample has a size n=150.

The sample proportion is p=0.86.

The standard error of the proportion is:

Then, we can calculate the z-statistic as:

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z<-1.497)=0.0672

As the P-value (0.0672) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 90% of all orders are mailed within 72 hours after they are received.

The null hypothesis is that 90% of all orders are shipped within 72 hours, denoted as H0: p = 0.90. The alternative hypothesis is that less than 90% of all orders are shipped within 72 hours, expressed as HA: p < 0.90.

### Explanation:

In hypothesis testing, the null hypothesis represents the theory that has been put forward, either because it is believed to be true or because it is used as a basis for argument. In this case, the null hypothesis would be that 90% of all orders are shipped within 72 hours. This can be formulated as H0: p = 0.90 where p represents the proportion of all orders shipped within 72 hours.

The alternative hypothesis on the other hand is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. Here, the alternative hypothesis would be that less than 90% of all orders are shipped within 72 hours. It can be expressed as HA: p < 0.90 where p remains the proportion of orders shipped within 72 hours.