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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Bill randomly selects a number from set A, and Sue randomly
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11 May 2020, 08:32
11 May 2020, 08:32
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Question Stats:
63% (01:50) correct
36% (02:26) wrong based on 33 sessions
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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?
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
Re: Bill randomly selects a number from set A, and Sue randomly
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12 May 2020, 20:09
12 May 2020, 20:09
1
Set A {1, 2, 3, 4, 5}; Probability of selecting anyone no from set A = 1/5
if the no selected by Bill is 1; the no selected by sue must be greater than 1, the probability of selecting no greater than 1, from Set B {1, 2, 3, 4, 5, 6, 7} = 6/7 (there are 6 no greater than 1)
the probability of selecting 1 by Bill and at the same time selecting >1 by Sue = 1/5 * 6/7
Similarly, probability of selecting 2 by Bill and at the same time selecting >2 by Sue = 1/5 * 5/7
Total possible required outcomes: selecting 1, 2, 3, 4 and 5 from set A; with selecting no >1, >2, >3, >4 and >5 from set B respectively.
Total possible required outcomes = (1/5 * 6/7) + (1/5 * 5/7) + (1/5 * 4/7) + (1/5 * 3/7) + (1/5 * 2/7)
= 1/5 * 20/7 = 4/7
if the no selected by Bill is 1; the no selected by sue must be greater than 1, the probability of selecting no greater than 1, from Set B {1, 2, 3, 4, 5, 6, 7} = 6/7 (there are 6 no greater than 1)
the probability of selecting 1 by Bill and at the same time selecting >1 by Sue = 1/5 * 6/7
Similarly, probability of selecting 2 by Bill and at the same time selecting >2 by Sue = 1/5 * 5/7
Total possible required outcomes: selecting 1, 2, 3, 4 and 5 from set A; with selecting no >1, >2, >3, >4 and >5 from set B respectively.
Total possible required outcomes = (1/5 * 6/7) + (1/5 * 5/7) + (1/5 * 4/7) + (1/5 * 3/7) + (1/5 * 2/7)
= 1/5 * 20/7 = 4/7
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Bill randomly selects a number from set A, and Sue randomly
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14 May 2020, 05:28
14 May 2020, 05:28
GreenlightTestPrep wrote:
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
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
