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Abhi077
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14 Oct 2018, 03:13
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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)!
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If there are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration, how many of the children are left-handed?
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
16 Oct 2018, 18:19
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Abhi077
If there are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration, how many of the children are left-handed?
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
Target question: How many of the children are left-handed?
Given: There are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration
Statement 1: The probability of no left-handed children being chosen is 3/7
P(no left-handers among those selected) = P(both right-handers among those selected)
So, P(both right-handers among those selected) = 3/7
In other words, P(1st selection is right-handed AND 2nd selection is right-handed) = 3/7
So, P(1st selection is right-handed) x P(2nd selection is right-handed) = 3/7
Let R = # of right-handers in the group
We can write: R/15 x (R - 1)/14 = 3/7
Simplify to get: (R² - R)/210 = 3/7
Cross multiply to get: 7(R² - R) = 3(210)
Divide both sides by 7 to get: R² - R = 3(30)
Or....: R² - R = 90
Then: R² - R - 90 = 0
Factor: (R - 10)(R + 9) = 0
So, EITHER R = 10 OR R = -9
Since R cannot be negative, we know that R = 10 (i.e., there are 10 right-handers)
If 10 children are right-handed, then 5 children are left-handed
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The number of left-handed children is less than the number of right handed children in the class
There are several scenarios that satisfy statement 2. Here are two:
Case a: There are 4 left-handers and 11 right-handers. In this case, the answer to the target question is there are 4 left-handers
Case b: There are 5 left-handers and 10 right-handers. In this case, the answer to the target question is there are 5 left-handers
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
General Discussion
14 Oct 2018, 04:47
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Abhi077
If there are 15 children in a gym class and 2 children are to be randomly chosen to perform a demonstration, how many of the children are left-handed?
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
1) The probability of no left-handed children being chosen is \(\frac{3}{7}\)
2) The number of left-handed children is less than the number of right handed children in the class
To help understand what we need to do, we'll translate the given data into equations.
This is a Precise approach.
We'll use 'x' to represent the number of left-handed children
(1) so 3/7 = prob of no left-handed = "ways to choose only right handed children" / "ways to choose children" =
(15-x)C2 / (15C2) = (15 - x)(14 - x) / (15*14).
This is complicated to solve precisely, but there is no need! There is at least one answer to this (quadratic) equation, and since changing x = "the number of left-handed children" must also change the probability of choosing a left-handed child, there can be only one applicable answer (the other one will be negative or too large or a fraction or something else irrelevant).
Sufficient.
(2) So x < 15 - x meaning that x < 7.5. With no additional information, x can be any of {1,2,3,4,5,6,7}.
Insufficient.
(A) is our answer.
