Events A, B, and C have the following probabilities of future

Question

Events A, B, and C have the following probabilities of future occurrence:

A: 20%

B: 50%

C: 80%

On the basis of these probabilities, select for  Both A and B  a description that must be true of the probability that both A and B will occur. And select for  B or C or Both  a description that must be true of the probability that B or C or both will occur. Make only two selections, one in each column.

ID: 101098

KarishmaB · Accepted Answer

I think of these as Sets questions, not probability. A = 20 B = 50 C = 80 (Total = 100) Select for Both A and B a description that must be true of the probability that both A and B will occur. If we were to calculate both A and B, it will have a maximum value of 20 because A itself is 20. So both cannot be more than that. ANSWER: Must be less than or equal to 20% And select for B or C or Both a description that must be true of the probability that B or C or both will occur If we were to calculate B or C or Both, this is our standard n(B or C) given by formula n(B or C) = n(B) + n(C) - n(Both) Recall we subtract Both because it is counted twice. ' Both B and C' will be maximum 50 because B is 50. So minimum value of B or C = 50 + 80 - 50 = 80 ANSWER: Must be greater than or equal to 80% In case there are any doubts in this method, check: https://youtu.be/HRnuURqGhmg https://youtu.be/oLKbIyb1ZrI

chetan2u · Answer

Both A and B  
P(A) = 20% and P(B) = 50%
 Maximum P(A&B)  - when A lies completely within B = 20%
 Minimum P(A&B)  - when there is no overlap = 0%
Answer:   Equal to or less than 20%

B or C or Both C and B  
P(C) = 80% and P(B) = 50%
 Maximum P(B or C or C&B)  - when certain portion of B, that is 20%, lies outside C = 100%
 Minimum P(B or C or C&B)  - when there is complete overlap = 80%
Answer:   Equal to or greater than 80%

demawtf · Answer

A: 20%

B: 50%

C: 80%

P(A&B) = 0,2 * 0,5 = 0,10 --> Must be less than or equal to 20%
P(B or C or both) = 0,5 + 0,8 - (0,5*0,8) = 0.9 --> Must be greater than or equal to 80%

TargetMBA007 · Answer

Thanks Karishma 
I am having difficulty making sense of this part
n(B or C) =  n(B) + n(C) - n(Both),
this comes to
= 50+80-(50*80) = 90% for me, and not 80%.

While I understand the ans. choice would still be valid, as when we state above 80%, it still covers 90%, but I wonder why you are getting 80% here and what I might be missingm, if I wanted to treat this purely as a probability Q and not a sets question.

@ KarishmaB

AIQ · Answer

Hi  KarishmaB ,

Thank you for the explanation. While I followed a similar train of thought when working on this problem, I was confused about whether I could assume that the universal set represents 100 (total probability is 100%). The question didn't provide any explicit conditions, or contexts, regarding these events, so I wasn't sure if events A, B, and C are part of the same universal set, (totaling 100%), or if A and B belong to one set while B and C belong to another. Essentially, your approach uses Venn Diagrams to calculate probability, which aligns with my thought process. However, I'm not sure how to define the universal set (S) and its relationship to these three events.

Adarsh_24 · Answer

I think you have assumed they are independent events.

deepshikhasuvi · Answer

hey, a slightly stupid question but why did you subtract the probability of both occurring (0.5*0.8). Not sure, but my natural instinct assumed it would be

this is obviously incorrect since the answer is like 170%

Bunuel · Answer

The solution you are referring to is not correct. Check correct solutions  HERE  and  HERE . Hope it helps.

Events A, B, and C have the following probabilities of future

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Both A and B	B or C or Both
		Must be equal to 40%
		Must be equal to 50%
		Must be equal to 70%
		Must be less than or equal to 20%
		Must be greater than or equal to 80%

GMAT Two-part Analysis (TPA) Questions

Events A, B, and C have the following probabilities of future

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