test01 wrote:
Carcass wrote:
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)
This is useful, and can you please mention what is y and what is b?
I thought about this and have an alternative approach.
Carcass please point out if I got it wrong:
P(A) = 3/4 and P(B) = 1/2.
And P(A U B) =1 (at max).
So, 3/4 + 1/2 - x = 1
=> x = 1/4
Now, P( A int B) = 3/4 * 1/2 = 3/8 = 0.375
So, 0.25 <= P(A int B) <= 0.375.
Opt C is the only one fitting in this range.