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For a certain probability experiment, the probability that

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For a certain probability experiment, the probability that [#permalink] New post 20 Jul 2018, 21:18
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For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20
[Reveal] Spoiler: OA
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Re: For a certain probability experiment, the probability that [#permalink] New post 20 Jul 2018, 23:13
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ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A-1/5
B-1/4
C-3/5
D-17/20



I am not exactly sure if this is the complete question. Single option correct questions have 5 options to choose from in the GRE.

Probability of event F= \(P(F)=\frac{1}{4}\)

Probability of event G= \(P(G)=\frac{3}{5}\)

Since nothing is mentioned if the events are independent or not we can write= P(F) and P(G)=\(P(F) \times P(G)=\frac{1}{4} \times \frac{3}{5}=\frac{3}{20}\).
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Re: For a certain probability experiment, the probability that [#permalink] New post 26 Oct 2019, 15:11
sandy wrote:
ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A-1/5
B-1/4
C-3/5
D-17/20



I am not exactly sure if this is the complete question. Single option correct questions have 5 options to choose from in the GRE.

Probability of event F= \(P(F)=\frac{1}{4}\)

Probability of event G= \(P(G)=\frac{3}{5}\)

Since nothing is mentioned if the events are independent or not we can write= P(F) and P(G)=\(P(F) \times P(G)=\frac{1}{4} \times \frac{3}{5}=\frac{3}{20}\).


It is talking about which could be the values P(F and G). We need to find the minimum possible value and the maximum possible value for this.
P(F and G ) will be minimum when F and G are mutually exclusive i.e value is 0. P(F and G ) will be maximum when least likely even is the subset of more likely event. In this case G is more likely, therefore F could be a subset of G hence making P(F and G ) = P(F) = 1/4. So, the values lying within this range should be possible values of P(F and G ).
Therefore, A and B are the answers.
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Re: For a certain probability experiment, the probability that [#permalink] New post 22 Apr 2020, 06:14
Im guessing the answer value should lie between 0 and 1/4 hence the options A), B) both are right.
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Re: For a certain probability experiment, the probability that [#permalink] New post 22 Apr 2020, 07:21
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Expert's post
ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20


We can also solve this question using the Double Matrix method

From the given information we can set up our matrix as follows:
Image
aside: the sum of all possible events must add to 1

Our goal will be to find the RANGE of possible values to go in the box denoted by the red star, since it represents the probability of both events happening.


Let's start by minimizing the value in the top left box.
The minimum possible value here is 0
When we complete the rest of matrix, we get the following:
Image
So 0 is the minimum possible probability of BOTH events occurring.


Now let's maximize the value in the top left box
Since about some of the two probabilities in the top row must add to 0.25, the maximum value that can go in the top left box is 0.25
When we complete the rest of the matrix, we get
Image
So 0.25 is the maximum possible probability of BOTH events occurring.


We can now conclude that the probability of both events occurring can range from 0 to 0.25

Answer choices A and B fall within that range

Answer: A, B

To learn more about the Double Matrix Method, watch this video:


Then you can try solving these two questions:
- https://greprepclub.com/forum/qotd-11-o ... -2660.html
- https://greprepclub.com/forum/on-a-cert ... 13470.html

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
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Re: For a certain probability experiment, the probability that [#permalink] New post 06 May 2020, 02:09
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The maximum value of F∩G when both sets are joined i.e. one is a subset of another. Here 3/5(P(G)) > 1/4(P(F)). Therefore P(F) is a subset of P(G).
Hence the maximum value of intersection will be 1/4.
The minimum value of F∩G will be obtained when both the sets are disjoint i.e 0.
Therefore, 0<=P(F∩G)<=1/4
So, the correct answers are A and B.
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Re: For a certain probability experiment, the probability that [#permalink] New post 08 May 2020, 04:17
sandy wrote:
ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A-1/5
B-1/4
C-3/5
D-17/20



I am not exactly sure if this is the complete question. Single option correct questions have 5 options to choose from in the GRE.

Probability of event F= \(P(F)=\frac{1}{4}\)

Probability of event G= \(P(G)=\frac{3}{5}\)

Since nothing is mentioned if the events are independent or not we can write= P(F) and P(G)=\(P(F) \times P(G)=\frac{1}{4} \times \frac{3}{5}=\frac{3}{20}\).


I don't agree

We multiply the individual probabilities only after we prove that the events are independent

We can also multiply in case of dependent events after factoring the dependence from the first event and accordingly changing the denominator/ numerator or both of the second fraction
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Re: For a certain probability experiment, the probability that [#permalink] New post 08 May 2020, 04:27
GreenlightTestPrep wrote:
ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20


We can also solve this question using the Double Matrix method

From the given information we can set up our matrix as follows:
Image
aside: the sum of all possible events must add to 1

Our goal will be to find the RANGE of possible values to go in the box denoted by the red star, since it represents the probability of both events happening.


Let's start by minimizing the value in the top left box.
The minimum possible value here is 0
When we complete the rest of matrix, we get the following:
Image
So 0 is the minimum possible probability of BOTH events occurring.


Now let's maximize the value in the top left box
Since about some of the two probabilities in the top row must add to 0.25, the maximum value that can go in the top left box is 0.25
When we complete the rest of the matrix, we get
Image
So 0.25 is the maximum possible probability of BOTH events occurring.


We can now conclude that the probability of both events occurring can range from 0 to 0.25

Answer choices A and B fall within that range

Answer: A, B

To learn more about the Double Matrix Method, watch this video:


Then you can try solving these two questions:
- https://greprepclub.com/forum/qotd-11-o ... -2660.html
- https://greprepclub.com/forum/on-a-cert ... 13470.html

Cheers,
Brent


Double matrix method as you have mentioned is to be used for over lapping sets

Why it doesn't apply here

If we draw a matrix

We get 4 quadrants

1. G and F

If we don't know dependence we can't go ahead

Same for the other three quadrants


2. G and Not F

3. F and Not G

4. Not F and Not G
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Re: For a certain probability experiment, the probability that [#permalink] New post 08 May 2020, 04:50
ssp4all wrote:
For a certain probability experiment, the probability that event F will occur is 1/4 and the probability that even G will occur is 3/5. Which of the following values could be the probability that the event F∩G (both) will occur?
A) 1/5
B) 1/4
C) 3/5
D) 17/20


P(F or G) = P(F) + P(G) - P(F and G)

P(F and G) = P(F) + P(G) - P(F or G)


P(F and G) = 1/4 + 3/5 - P(F or G)

P(F and G) = 17/20 - P(F or G)

Maximum value for P(F or G) will be 17/20 (when F and G are mutually exclusive)

Therefore

Minimum value of P(F and G) will be zero

Maximum value of P(F and G) will be 3/5 = 12/20 (when F is a subset of G)


Let's look at the Options

1/5 = 4/20 -> Possible

1/4 = 5/20 -> possible

3/5 = 12/20 -> not possible

17/20 -> not possible
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Re: For a certain probability experiment, the probability that   [#permalink] 08 May 2020, 04:50
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