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11 May 2020, 06:42
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:06) correct
29%
(02:12)
wrong
based on 226
sessions
History
Date
Time
Result
Not Attempted Yet
Set A {1, 2, 3, 4, 5}
Set B {1, 2, 3, 4, 5, 6, 7}
Bill randomly selects a number from set A, and Sue randomly selects a number from set B. What is the probability that Sue’s number is greater than Bill’s number?
A) 4/7
B) 7/12
C) 3/5
D) 2/3
E) 5/7
Set B {1, 2, 3, 4, 5, 6, 7}
Bill randomly selects a number from set A, and Sue randomly selects a number from set B. What is the probability that Sue’s number is greater than Bill’s number?
A) 4/7
B) 7/12
C) 3/5
D) 2/3
E) 5/7
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11 May 2020, 09:30
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BrentGMATPrepNow
When we solve this probability question using counting techniques, we quickly see it's a lot of work to (accurately) list and count all the possible outcomes in which Sue's number is greater than Bill's number.
Here's a technique that you may be able to apply with other questions requiring listing in accounting.
GIVEN: Set A {1, 2, 3, 4, 5} and Set B {1, 2, 3, 4, 5, 6, 7}
We're selecting one number from the 5 numbers in set A
And we're selecting one number from the 7 numbers in set B
So, the total number of possible outcomes = (5)(7) = 35
To determine the number of outcomes in which Sue's number is greater than Bill's number, we can create a table that looks like this:
Note: each of the 35 boxes represents one possible outcome.
For example, the box with the star (below) represents the outcome in which Bill select the 1 from set A, and Sue selects the 2 from set B
So, if we place a star in every box in which Sue's number is greater than Bill's number, we get:
So the total number of outcomes in which Sue's number is greater than Bill's number = 1 + 2 + 3 + 4 + 5 + 5 = 20
So, P(Sue's number is greater than Bill's number) = 20/35 = 4/7
Answer: A
Cheers,
Brent
General Discussion
11 May 2020, 08:19
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Set A {1, 2, 3, 4, 5}
Set B {1, 2, 3, 4, 5, 6, 7}
Bill randomly selects a number from set A, and Sue randomly selects a number from set B. What is the probability that Sue’s number is greater than Bill’s number?
method I :
total number of cases : (1,1) ; (1,2) ; (1,3) ; (1,4) ; (1,5) ; (1,6) ; (1,7) ; (2,1) ; (2,2) ; (2,3) ; (2,4) ; (2,5) ; (2,6) ; (2,7) ; (3,1) ; (3,2) ; (3,3) ; (3,4) ; (3,5) ; (3,6) ; (3,7) ; (4,1) ; (4,2) ; (4,3) ; (4,4) ; (4,5) ; (4,6) ; (4,7) ; (5,1) ; (5,2) ; (5,3) ; (5,4) ; (5,5) ; (5,6) ; (5,7) ;
= n(A) * n(B)
=5*7
=35
now,Sue’s number is greater than Bill’s number = (1,2) ; (1,3) ; (1,4) ; (1,5) ; (1,6) ; (1,7) ; (2,3) ; (2,4) ; (2,5) ; (2,6) ; (2,7) ;(3,4) ; (3,5) ; (3,6) ; (3,7) ; (4,5) ; (4,6) ; (4,7) ; (5,6) ; (5,7) ;
=6+5+4+3+2
=20
therefore, required probability = 20/35 = 4/7
correct answer A
method II :
the probability that Sue’s number is greater than Bill’s number
= P(getting 1)*P(getting >1)+P(getting 2)*P(getting >2)+P(getting 3)*P(getting >3)+P(getting 4)*P(getting >4)+P(getting 5)*P(getting >5)
= 1/5 *6/7 + 1/5 *5/7 + 1/5 *4/7 + 1/5 *3/7 + 1/5 *2/7
=6/35+5/35+4/35+3/35+2/35
=20/35
correct answer A
method III :
the probability that Sue’s number is greater than Bill’s number
=1- the probability that Sue’s number is less than or equal to Bill’s number
=1- [P(getting 1)*P(getting ≤1)+P(getting 2)*P(getting ≤2)+P(getting 3)*P(getting ≤3)+P(getting 4)*P(getting ≤4)+P(getting 5)*P(getting ≤5)]
=1-[1/5*1/7+1/5*2/7+1/5*3/7+1/5*4/7+1/5*5/7]
=1-[1/35+2/35+3/35+4/35+5/35]
=1-15/35
=20/35
correct answer A
Set B {1, 2, 3, 4, 5, 6, 7}
Bill randomly selects a number from set A, and Sue randomly selects a number from set B. What is the probability that Sue’s number is greater than Bill’s number?
method I :
total number of cases : (1,1) ; (1,2) ; (1,3) ; (1,4) ; (1,5) ; (1,6) ; (1,7) ; (2,1) ; (2,2) ; (2,3) ; (2,4) ; (2,5) ; (2,6) ; (2,7) ; (3,1) ; (3,2) ; (3,3) ; (3,4) ; (3,5) ; (3,6) ; (3,7) ; (4,1) ; (4,2) ; (4,3) ; (4,4) ; (4,5) ; (4,6) ; (4,7) ; (5,1) ; (5,2) ; (5,3) ; (5,4) ; (5,5) ; (5,6) ; (5,7) ;
= n(A) * n(B)
=5*7
=35
now,Sue’s number is greater than Bill’s number = (1,2) ; (1,3) ; (1,4) ; (1,5) ; (1,6) ; (1,7) ; (2,3) ; (2,4) ; (2,5) ; (2,6) ; (2,7) ;(3,4) ; (3,5) ; (3,6) ; (3,7) ; (4,5) ; (4,6) ; (4,7) ; (5,6) ; (5,7) ;
=6+5+4+3+2
=20
therefore, required probability = 20/35 = 4/7
correct answer A
method II :
the probability that Sue’s number is greater than Bill’s number
= P(getting 1)*P(getting >1)+P(getting 2)*P(getting >2)+P(getting 3)*P(getting >3)+P(getting 4)*P(getting >4)+P(getting 5)*P(getting >5)
= 1/5 *6/7 + 1/5 *5/7 + 1/5 *4/7 + 1/5 *3/7 + 1/5 *2/7
=6/35+5/35+4/35+3/35+2/35
=20/35
correct answer A
method III :
the probability that Sue’s number is greater than Bill’s number
=1- the probability that Sue’s number is less than or equal to Bill’s number
=1- [P(getting 1)*P(getting ≤1)+P(getting 2)*P(getting ≤2)+P(getting 3)*P(getting ≤3)+P(getting 4)*P(getting ≤4)+P(getting 5)*P(getting ≤5)]
=1-[1/5*1/7+1/5*2/7+1/5*3/7+1/5*4/7+1/5*5/7]
=1-[1/35+2/35+3/35+4/35+5/35]
=1-15/35
=20/35
correct answer A
