Question

In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 51% majored in business or commerce; 18% majored in engineering; 17% majored in the social sciences; 7% majored in the sciences; 4% majored in the humanities; and 3% listed some major other than the preceding. Assume there are no double majors. (a) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.) P= (BLANK)% Select the probability rule you used to find the answer. A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A). B.) Rule 2. If S is the sample space in a probability model, then P(S) = 1. C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B). D.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. (b) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.) P= (BLANK)% Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce. A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A). B.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B). D.) Rule 2. If S is the sample space in a probability model, then P(S) = 1.

Name: 1 in many settings the rules of probability are just basic facts about percents the graduate management admission test gmat website provides information about the undergraduate majors of tho 45713
Uploaded: 2021-12-20T17:06:02-08:00
Duration: 7 min 21 s
Channel: Sheryl Ezze
Description: 1 in many settings the rules of probability are just basic facts about percents the graduate management admission test gmat website provides information about the undergraduate majors of tho 45713

          In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 51% majored in business or commerce; 18% majored in engineering; 17% majored in the social sciences; 7% majored in the sciences; 4% majored in the humanities; and 3% listed some major other than the preceding. Assume there are no double majors.

(a) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.)
P= (BLANK)%
Select the probability rule you used to find the answer.
A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A).
B.) Rule 2. If S is the sample space in a probability model, then P(S) = 1.
C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B).
D.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1.

(b) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.)
P= (BLANK)%
Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce.
A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A).
B.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1.
C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B).
D.) Rule 2. If S is the sample space in a probability model, then P(S) = 1.

Added by Courtney H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

12/20/2021

Step 1

Given: Probability of engineering = 18% Probability of sciences = 7% Probability of engineering or sciences = Probability of engineering + Probability of sciences - Probability of engineering and sciences Probability of engineering or sciences = 18% + 7% - Show more…

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In many settings, the "rules of probability" are just basic facts about percents. The Graduate Management Admission Test (GMAT) website provides information about the undergraduate majors of those who took the test in specific years. Suppose that in a certain year: 51% majored in business or commerce; 18% majored in engineering; 17% majored in the social sciences; 7% majored in the sciences; 4% majored in the humanities; and 3% listed some major other than the preceding. Assume there are no double majors. (a) What percent of those who took the test in this certain year majored in either engineering or the sciences? (Enter your answer as a percent and as a whole number.) P= (BLANK)% Select the probability rule you used to find the answer. A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A). B.) Rule 2. If S is the sample space in a probability model, then P(S) = 1. C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B). D.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. (b) What percent of those who took the test in this certain year majored in something other than business or commerce? (Enter your answer as a percent and as a whole number.) P= (BLANK)% Select the probability rule you used to find the percentage of undergraduates who majored in something other than business or commerce. A.) Rule 4. For any event A, P(A does not occur) = 1 - P(A). B.) Rule 1. The probability P(A) of any event A satisfies 0 ≤ P(A) ≤ 1. C.) Rule 3. Two events A and B are disjoint if they have no outcomes in common and so can never occur together. If A and B are disjoint, P(A or B) = P(A) + P(B). D.) Rule 2. If S is the sample space in a probability model, then P(S) = 1.

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00:01 You actually have three questions in one here.

00:02 So that first question, we know that the probability of a is 0 .65, and the probability of b is given to be 0 .77.

00:13 And the probability of at least one of them, which means at least one means a or b is equal to 0 .9.

00:22 And so we want to find the probability of a and b.

00:26 We want to find are they mutually exclusive and we want to find are they independent? and so we know this statement is true for all union events.

00:40 Probability of a or b is equal to the probability of a plus the probability of b minus the probability of the a and b.

00:49 And so we know 0 .9 is equal to 0 .65 plus 0 .44 minus the intersection of these two, which is what we want to find of a and b.

01:04 And so doing our algebra on this, basically i'll end up, if i get this on this side, i'll get that probability of a and b equaling 0 .65 plus 0 .77 minus 0 .9.

01:20 And 0 .65 plus 0 .77 minus 0 .9 gives me a total of 0 .52 .6 .5.

01:28 So the intersection of those is .52, which means, no, they're not mutually exclusive because they can happen at the same time.

01:37 Independent, well, our test for independent is, let's find what the product is of these two.

01:44 Because if the product of these two, the 0 .65 times .77, if that product, that product is .505, and that does not equal the probability of the intersection.

01:56 So no, they're not independent.

01:58 They're not far from it, but they are not independent.

02:02 Now, question two.

02:04 Question two, you were dealing with passing, and the probability of passing first class is 0 .835.

02:13 Probability of passing, well, we want to find that.

02:17 Probability of passing both classes is 0 .276, and the probability of passing at least one of them, which means a or b.

02:31 So at least one means you either pass a or b or possibly both, and that's 0 .981.

02:37 And we have exactly the same scenario.

02:39 We want to use that union formula.

02:42 So 0 .981 is equal to the probability of a plus the probability of b, which we don't know, minus the intersection, which is this 0 .76.

02:55 So if we take the .981 and subtract away .835 and add, we'll get that to the other side that's adding on, add on, oops i didn't put the right symbol in there.

03:10 I got to insert a subtraction, otherwise we're going to have an issue.

03:14 And then add on the .276.

03:20 .276.

03:21 And that comes out to be the probability of b is equal to point 422.

03:28 So there's your first answer.

03:30 And then we wanted to find out are they mutually exclusive? and the answer is no.

03:35 Before there's an intersection...

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