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Events A, B, C and D are all possible outcomes of an experiment. In t

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Math Revolution GMAT Instructor
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Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 11 Apr 2018, 05:54
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A
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[GMAT math practice question] 4.11

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4.11.png
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Events \(A, B, C\) and \(D\) are all possible outcomes of an experiment. In the table above, \(P(x)\) denotes the probability that event \(x\) occurs. What is \(P(A)\)?

\(1) P(A)+P(B)+P(C)=0.75\)
\(2) P(C)+P(D)=0.25\)

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Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 11 Apr 2018, 07:06
total probability is 1
therefore, a+c+d=0.75

St1
a+0.25+c=0.75
a=0.5-c
Insufficient

St2
c+d=0.25
and we know that
a+c+d=0.75
a=0.5
Sufficient
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Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 13 Apr 2018, 02:36
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since \(P(A) = a = 1 – ( c + d ) – 0.25 = 0.75 – (c + d)\), then \(P(A)\) can be determined from the value of \(c + d\). Thus, the answer is \(B\).

Condition 1)
If \(P(A) = 0.5, P(B) = 0.25\) and \(P(C) = 0\), then we have \(P(A) = 0.5.\)
If \(P(A) = 0.4, P(B) = 0.25\) and \(P(C) = 0.1\), then we have \(P(A) = 0.4.\)
Thus, condition 1) is not sufficient.

Condition 2)
Since \(P(A) + P(B) + P(C) + P(D) = 1, P(B) = 0.25\) and \(P(C) + P(D) = 0.25\) from condition 2), we have \(P(A) = 0.5.\)
Thus, condition 2) is sufficient.

Therefore, the answer is B.
Answer: B
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Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 25 Apr 2018, 23:03
P(x)=P(a)+P(b)+P(c)+P(d)=1
=P(a)+P+0.25+P(c)+P(d)=1
=P(a)+P(c)+P(d)=0.75

Require c and d values

B clearly gives this Vue, A does not
So B is aNswer

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Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 21 Sep 2018, 23:43
MathRevolution wrote:
[GMAT math practice question] 4.11

Attachment:
4.11.png


Events \(A, B, C\) and \(D\) are all possible outcomes of an experiment. In the table above, \(P(x)\) denotes the probability that event \(x\) occurs. What is \(P(A)\)?

\(1) P(A)+P(B)+P(C)=0.75\)
\(2) P(C)+P(D)=0.25\)



Looking at St. 1 -
We know that P(B)=.25
and from the st. P(A)+P(B)+P(C)=0.75

So, P(A)+P(C) =.25

No other way to find out the value of P(A).
Insufficient

So, options A & D are out


Now, for st.2
P(C)+P(D)=0.25
and it is given that P(B)=.25

Now, we also know that

P(A)+P(B)+P(C)+P(D)=1

replacing the values,

P(A)+.25+.5=1

P(A) =.25

Hence, B


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Re: Events A, B, C and D are all possible outcomes of an experiment. In t  [#permalink]

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New post 22 Sep 2018, 22:57
First of all, I am not that good at probability. So please let me know if my approach is correct or not.

We need to P(A).

St 1: P(A)+P(B)+P(C)=0.75
=>P(B) = 0.25
=>P(A) + P(B) = 0.50
=> We cannot determine the value of P(A) from the given data. Hence insufficient.

St 2: P(C) + P(D) = 0.25
=>P(A)+P(B)+P(C)+P(D)=1
=>P(A)+0.25+0.25=1
=>P(A)=1-0.25-0.25
=>P(A)=0.50

Hence I chose B
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Re: Events A, B, C and D are all possible outcomes of an experiment. In t &nbs [#permalink] 22 Sep 2018, 22:57
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