For a certain probability experiment, the probability that Event A wil

Question

For a certain probability experiment, the probability that Event A will occur is \(\frac{3}{4}\) and probability that Event B will occur is \(\frac{1}{2}\). Which of the following values could be the probability that Event A∩B will occur?

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{3}\)

D. \(\frac{2}{3}\)

E. \(\frac{3}{4}\)

A.  \frac{1}{6}

B.  \frac{1}{5}

C.  \frac{1}{3}

D.  \frac{2}{3}

E.  \frac{3}{4}

Regor60 · Answer

See attached.

The short answer is that the maximum value is limited by the lower of 3/4 and 1/2, so D&E are eliminated.

Testing A,B and C indicates that both A and B require a negative value for the probability of neither event happening in order for the probability space to sum to 1, but that C is viable with the probability of neither event occurring at 1/12

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Jshellypp · Answer

I dont even know where to start with this one. Can anyone break it down? I dont even get how the explanation above even started.

yeallah · Answer

Bunuel  can you help?

Dhananjayrai · Answer

In this question, the best approach is elimination imo.
Since, the maximum value p(a)*p(b) can take is 1/2, option D and E are eliminated.
Secondly, the least value that p(a)*p(b) can take is -> ( 3/4+1/2) - 1 = 1/4, so option A and B are eliminated and we are left with C as the answer.
Hope this helps.

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SatvikVedala · Answer

Hi

Let me answer my approach

1 = P(AUB) + P(A'∩B')  
1 = P(A)+P(B)-P(A∩B)+P(A'∩B')
1 = 3/4 + 1/2-P(A∩B)+P(A'∩B')
1 - 5/4 = -P(A∩B)+P(A'∩B')
1/4 = P(A∩B)-P(A'∩B')
1/4+P(A'∩B') = P(A∩B)

for P(A∩B) to be minimum P(A'∩B') must be minimum, considering P(A'∩B') as 0 => 1/4 = P(A∩B)
also from the question we have P(A) as 3/4 & P(B) as 1/2 so the Maximum value of P(A∩B) is 1/2

0.25<= P(A∩B) <= 0.5

as per the options C suits

paridhi987 · Answer

How did you calculate the least value?

bumpbot · Answer

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For a certain probability experiment, the probability that Event A wil

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For a certain probability experiment, the probability that Event A wil

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