(Solved) Out of 20 students taking a midterm exam, 15 answered the fi rst of two bonus questions, 13 answered

tofurky1975

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10 years ago

Out of 20 students taking a midterm exam, 15 answered the fi rst of two bonus questions, 13 answered

Out of 20 students taking a midterm exam, 15 answered
the fi rst of two bonus questions, 13 answered
the second bonus question, and 2 answered neither
bonus question. How many students answered both
bonus questions?

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padre

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10 years ago

I am going to assume you are up to karnaugh maps, if not this isnt going to make a lot of sense.

lets make A= the probability of getting the first answer and
B= the probability of getting the second answer

now you need to set the problem up in a pnnet like so:

A A(not)
B
B(not)

now basically this works using the intersects with everything adding up to the 20 students, here is the information you gave me:

A A(not)
B 13
B(not) 2
15 20

now it is just a matter of subtraction
20-x=15 is at the end of A(not)
x=5
y+ 2 = 5 is intersecting B and A(not)
y=3
finally 13 - 3 = 10 which intersects A and B
which is your answer (i hope)

if you need to know more about intersects simply look at wikipedia, all you really need to know is it works by analysing a venn diagram AnB(not) is what is in A but not in B

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bio_man

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doubleu

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10 years ago

Assign each student a letter from A through T (the 20th letter of the alphabet).
Assign letters A - O (students 1 - 15) to question 1.
Assign letters S and T (students 19 and 20) to "neither".
Assign letters P, Q, R, and 10 more (A - J) to question 2, since P, Q, and R are the only students as of yet unaccounted for, and since 13 students answered question 2.

1 - ABCDEFGHIJKLMNO
2 - PQRABCDEFGHIJ
neither - ST

You can see that students A - J answered both questions. Therefore, your answer is that 10 students answered both questions.

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vanbu

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10 years ago

Out of 15 students some of them also answered question 2.
Out of 13 students some of them also answered question 1.

Let the students who answered both the question = x
Then,
The students who only answered 1st bonus question = 15 - x
The students who only answered 2nd bonus question = 13 - x
The students who answered neither of the bonus questions = 2 .... (Given)
Now,
Students whon answered only 1st bonus question + Students who answered only 2nd Question + Student who answered both the questions + Students who did not answer any question = Total Students
So,
(15-x) + (13-x) + (x) + 2 = 20
Or,
28 - x = 18
Or,
28 = x + 18
Or,
x + 18 = 28
Or, x = 10 (ur answer)

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Alexx

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