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For a certain probability experiment, the probability that Event A wil
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25 Aug 2023, 02:59
25 Aug 2023, 02:59
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For a certain probability experiment, the probability that Event A will occur is 3/4 and probability that Event B will occur is 1/2. Which of the following values could be the probability that Event A ∩ B will occur?
Indicate all that apply
A. 1/6
B. 1/5
C. 1/3
D. 2/3
E. 3/4
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Indicate all that apply
A. 1/6
B. 1/5
C. 1/3
D. 2/3
E. 3/4
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: For a certain probability experiment, the probability that Event A wil
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11 Sep 2023, 06:35
11 Sep 2023, 06:35
Can you please explain this?
Thanks
Posted from my mobile device
Thanks
Posted from my mobile device
Re: For a certain probability experiment, the probability that Event A wil
[#permalink]
18 Sep 2023, 08:29
18 Sep 2023, 08:29
1
Expert Reply
OE
Let us make a table structure for this question:
We are given that, P (A) = 3/4; hence P (A does not occur) = 1 −3/4=1/4
Also, P (B occurs) is given as 1/2
Therefore, P (B does not occur) = 1 −1/2=1/2
We need to find AꓵB; i.e. both A occurs and B occurs.
To find minimum value of AꓵB (𝑥); let us maximize 𝑦.
We know, 𝑥 + 𝑦 =1/2
and 𝑦 + 𝑏 =1/4
The minimum value 𝑏 can have is 0 in that case 𝑦 =1/4
Hence, minimum 𝑥 =1/4
To find maximum value of 𝑥, let us minimize 𝑦.
We know, 𝑥 + 𝑦 =1/2
and 𝑦 + 𝑏 =1/4
The maximum value 𝑏 can have is 1/4 in that case 𝑦 = 0.
Therefore, maximum value of 𝑥 =1/2.
Therefore, AꓵB varies from 1/4 to 1/2.
From the options provided 1/3
is the only value which lies between 1/4 to 1/2
Ans. (C)
Let us make a table structure for this question:
We are given that, P (A) = 3/4; hence P (A does not occur) = 1 −3/4=1/4
Also, P (B occurs) is given as 1/2
Therefore, P (B does not occur) = 1 −1/2=1/2
We need to find AꓵB; i.e. both A occurs and B occurs.
To find minimum value of AꓵB (𝑥); let us maximize 𝑦.
We know, 𝑥 + 𝑦 =1/2
and 𝑦 + 𝑏 =1/4
The minimum value 𝑏 can have is 0 in that case 𝑦 =1/4
Hence, minimum 𝑥 =1/4
To find maximum value of 𝑥, let us minimize 𝑦.
We know, 𝑥 + 𝑦 =1/2
and 𝑦 + 𝑏 =1/4
The maximum value 𝑏 can have is 1/4 in that case 𝑦 = 0.
Therefore, maximum value of 𝑥 =1/2.
Therefore, AꓵB varies from 1/4 to 1/2.
From the options provided 1/3
is the only value which lies between 1/4 to 1/2
Ans. (C)
