If the probability for A to fail in an examination is 0.2 and that for

Question

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails, is

(A) 0.38 
(B) 0.44
(C) 0.50 
(D) 0.56
(E) 0.94

Kinshook · Answer

Asked: If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails, is

Probability that both A & B pass = (1-.2)*(1-.3) = .8*.7 = .56
Probability that either A or B fails = 1 - .56 = .44

IMO B

ParitoshRawat99 · Answer

P(Either A or B) = P(A) + P(B) - P(A and B occur together)

According to the question. 
P(Either A fails or B fails) = 0.2 + 0.3 - 0.06
 Answer = 0.44

prithak · Answer

This seems to be incorrect. .44 takes into consideration the case where both fail, which is not the question. Can you please clarify if my understanding is inccorect!

MathRevolution · Answer

P(A) = 0.2 
 P(A') = 0.8

P(B) = 0.3 
 P(B') = 0.7

P(either A or B fails) = 1- Both pass = 1 -  (0.8 * 0.7)  = 1 -  0.56  =  0.44

Answer B

Gknight5603 · Answer

but the question is not asking about the probability of both failing the test together.
its just asking for the probability of one passing and other to fail.

1- both pass ....will include the event when both fails

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NipunSyn · Answer

I have a doubt. The question asks for "probability that either A or B fails". There is no mention of the joint case. So the probability should be 
p = p(A passes and B fails) + p(A fails and B passes) 
p = 0.2*0.7 + 0.8*0.3
p = 0.38

Shouldn't the correct choice be A? Why have we considered the case where A and B both fail together?

Vibhatu · Answer

P(Either A or B) = P(A) + P(B) - P(A and B occur together)

Therefore...
P(Either A fails or B fails) = 0.2 + 0.3 - 0.06
Answer: 0.44 (B)

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Bunuel · Answer

In mathematics, 'or', unless explicitly specified otherwise, means an inclusive 'or', encompassing both condition 1, condition 2, or both conditions.

ajit23 · Answer

Inclusive OR: This includes the cases where either A fails, or B fails, or both A and B fail.
Exclusive OR: This includes only the cases where either A fails or B fails, but not both.
In typical probability problems, unless explicitly stated otherwise, "either A or B" usually refers to the inclusive OR. This means we consider the probability of A failing, B failing, or both failing.

pierjoejoe · Answer

in your solution you should consider all the possibilities (as  Bunuel  said)
A passes B fails --> 0.2*0.7 = 0.14
A fails B passes --> 0.8*0.3 = 0.24
A fails B fails --> 0.3*0.2 = 0.06

total is 0.44

but it is way simpler to consider the exact opposite, what is the probability of both of them passing the exam?
P(A pass) = 1-0.2
P(B pass) = 1-0.3
P(A pass AND B pass) = P(A pass)*P(B pass) = 0.8*0.7 = 0.56
so the probability of either of them NOT passing the exam is the exact complement --> 1-0.56 = 0.44

If the probability for A to fail in an examination is 0.2 and that for

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