Question

In a lottery game, a single ball is drawn at random from a con- tainer that contains 25 identical balls numbered from 1 through 25. In Problems 25-32, use equation (1) to compute the probabil- ity that the number drawn is 25. Odd or a multiple of 4 26. Even or a multiple of 7 27. Prime or greater than 20 28. Less than 10 or greater than 10 29. A multiple of 2 or a multiple of 5 30. A multiple of 3 or a multiple of 4 31. Less than 5 or greater than 20 32. Prime or less than 14 33. If the probability is .51 that a candidate wins the election, what is the probability that he loses? 34. If the probability is .03 that an automobile tire fails in less than 50,000 miles, what is the probability that the tire does not fail in 50,000 miles?

          In a lottery game, a single ball is drawn at random from a con-
tainer that contains 25 identical balls numbered from 1 through
25. In Problems 25-32, use equation (1) to compute the probabil-
ity that the number drawn is
25. Odd or a multiple of 4
26. Even or a multiple of 7
27. Prime or greater than 20
28. Less than 10 or greater than 10
29. A multiple of 2 or a multiple of 5
30. A multiple of 3 or a multiple of 4
31. Less than 5 or greater than 20
32. Prime or less than 14
33. If the probability is .51 that a candidate wins the election,
what is the probability that he loses?
34. If the probability is .03 that an automobile tire fails in less
than 50,000 miles, what is the probability that the tire does
not fail in 50,000 miles?

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In a lottery game, a single ball is drawn at random from a con-
tainer that contains 25 identical balls numbered from 1 through
25. In Problems 25-32, use equation (1) to compute the probabil-
ity that the number drawn is
25. Odd or a multiple of 4
26. Even or a multiple of 7
27. Prime or greater than 20
28. Less than 10 or greater than 10
29. A multiple of 2 or a multiple of 5
30. A multiple of 3 or a multiple of 4
31. Less than 5 or greater than 20
32. Prime or less than 14
33. If the probability is .51 that a candidate wins the election,
what is the probability that he loses?
34. If the probability is .03 that an automobile tire fails in less
than 50,000 miles, what is the probability that the tire does
not fail in 50,000 miles?

Added by John J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert T. L.

07/19/2022

Step 1

Favorable outcomes: - Odd numbers: There are 13 odd numbers from 1 to 25 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25). - Multiples of 4: There are 6 multiples of 4 from 1 to 25 (4, 8, 12, 16, 20, 24). Total possible outcomes: There are 25 balls in total. Show more…

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Texts: numbers 25, 27, 31, 33 In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problems 25-32, use equation 1 to compute the probability that the number drawn is: 25. Odd or a multiple of 4 26. Even or a multiple of 7 27. Prime or greater than 20 28. Less than 10 or greater than 10 29. A multiple of 2 or a multiple of 5 30. A multiple of 3 or a multiple of 4 31. Less than 5 or greater than 20 32. Prime or less than 14 33. If the probability is 51 that a candidate wins the election, what is the probability that he loses? 34. If the probability is 0.3 that an automobile tire fails in less than 50,000 miles, what is the probability that the tire does not fail in 50,000 miles?

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Transcript

00:01 Hey there, welcome to numerate.

00:03 So we are given the tire lifetimes of an automobile.

00:07 So with that, the lifetimes are normally distributed as given, and we are given the population mean and standard deviation.

00:15 And we had to find the following probabilities and proportions.

00:19 So with this, we're going to do a first.

00:25 So a, we have, what is the probability that i randomly selected tire has lifetime greater than 48? so with our given mean and standard deviation, let's write it down first.

00:39 Population mean is denoted as mule, which is 39, and we have our population standard deviation, which is denoted sigma here, which is basically 4.

00:56 So our probability we're looking for for part a is p of x is greater than 48 would be our probability function here.

01:09 All right, p of x is greater than 48.

01:13 We will have to calculate our z square heritude in order to find a probability.

01:18 Z equals x values of 48, minus our mean 39, divided by our standard deviation, 4.

01:28 We're going to calculate this and see what value we get.

01:32 And you should end up a value of 2 .25.

01:36 Now, to find a probability, you can use a z -score probability table, or you can use a calculator.

01:44 So, but you should get a probability of around 0 .01 to 2.

01:53 Right, rounded to four decimal places here.

01:56 Let me see.

01:57 Yep, four decimal places.

02:02 All right.

02:03 And then let's do part b.

02:05 So part b says, what's the proportion of tires that have lifetimes between 38 and 43? so that proportion, we still denoted as probability, where x is between 38, and 43...

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