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exc4libur
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There is a 50% chance Jen will visit Chile this year, while there is a 26 Jan 2020, 13:12
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Bunuel
There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?[/b]

A. 25%
B. 50%
C. 62.5%
D. 63.5%
E. 75%
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p(c)=50%≠50%
p(m)=25%≠75%
p(c≠m)=1/2*3/4=3/8
p(m≠c)=1/4*1/2=1/8
OR=ADD: 3/8+1/8=1/2

Ans (B)
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There is a 50% chance Jen will visit Chile this year, while there is a 14 Jun 2020, 01:29
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VeritasKarishma
Bunuel
There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year. What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?[/b]

A. 25%
B. 50%
C. 62.5%
D. 63.5%
E. 75%


This question was written to help people understand the use of sets in probability. Think of the venn diagram with two overlapping sets.

n(A or B) = n(A) + n(B) - n(A and B) ........(I)
(We subtract n(A and B) because it is double counted. The overlapping part was counted twice, once in each circle so it is subtracted out.)

n(A or B but not Both) = n(A) + n(B) - n(A and B) - n(A and B) ............(II)
(We subtract another n(A and B) so that 'Both' is subtracted out. The overlapping part was counted once in (I); now it is totally removed)

P (visit C or M but not Both) = 1/2 + 1/4 - (1/2*1/4) - (1/2*1/4) = 1/2

Answer (B)
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This solution assumes that going to Chile and Madagascar are independent events and hence the P(Going to C and M) is = (1/2*1/4). However, it is not certain from the question whether the two events are independent. It may be possible that if Jen goes to Chile, the probability of going to Madagascar drops to 0.15 instead of 0.25 ?
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There is a 50% chance Jen will visit Chile this year, while there is a 16 Dec 2020, 04:03
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What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?

The word 'or' means ADD.

P(Chile)*P(Not Madagascar) + P(Not Chile)*P(Madagascar)

1/2 * 3/4 + 1/2 * 1/4 = 3/8 + 1/8 = 4/8 = 50%
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There is a 50% chance Jen will visit Chile this year, while there is a 14 Oct 2025, 22:13
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Can experts can clarif this pls

'Either A or B ' - It means A or B but not both (i.e A but not B + B but not A)

'A or B' - It means only A + Both + Only B
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There is a 50% chance Jen will visit Chile this year, while there is a 14 Oct 2025, 22:34
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It's the second one. That's why the question has to specify "but not both."

In daily speech, "or" can sometimes be exclusive. For instance, if a contest offers a prize of "a new car or $30,000," you can't choose to take both. But in most cases, and especially in math and logic, "or" is inclusive, meaning that includes the possibility of either or both options unless stated otherwise.
BKD5050
Can experts can clarif this pls

'Either A or B ' - It means A or B but not both (i.e A but not B + B but not A)

'A or B' - It means only A + Both + Only B
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There is a 50% chance Jen will visit Chile this year, while there is a 14 Oct 2025, 22:45
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Thank you for your response.

Do you mind answering to below Q. Its a gmatclub Q.

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

A. 41/50
B. 9/50
C. 6/50
D. 21/25
E. 8/25

The actual answer stated in GMATclub is 41/50. However, if we dont consider 'both' I am getting 27/50 which is not stated in the options. Its 'either or' mentioned in the Q so It should'nt include 'both' right?
DmitryFarber
It's the second one. That's why the question has to specify "but not both."

In daily speech, "or" can sometimes be exclusive. For instance, if a contest offers a prize of "a new car or $30,000," you can't choose to take both. But in most cases, and especially in math and logic, "or" is inclusive, meaning that includes the possibility of either or both options unless stated otherwise.

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There is a 50% chance Jen will visit Chile this year, while there is a 14 Oct 2025, 23:21
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No, "either/or" is the same as "or." It includes the possibility of both. We only exclude the possibility of both if we are explicitly told to do so. If I buy a defective car and say "I want either a refund or a replacement vehicle," I won't *expect* both, but getting both would still satisfy my demand!
BKD5050
Thank you for your response.

Do you mind answering to below Q. Its a gmatclub Q.

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

A. 41/50
B. 9/50
C. 6/50
D. 21/25
E. 8/25

The actual answer stated in GMATclub is 41/50. However, if we dont consider 'both' I am getting 27/50 which is not stated in the options. Its 'either or' mentioned in the Q so It should'nt include 'both' right?

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There is a 50% chance Jen will visit Chile this year, while there is a 15 Oct 2025, 02:40
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There is a 50% chance Jen will visit Chile this year, while there is a 25% chance that she will visit Madagascar this year.

What is the probability that Jen will visit either Chile or Madagascar this year, but NOT both?

The probability that Jen will visit either Chile or Madagascar this year, but NOT both = (The probability that Jen will visit Chile and not Madagascar) + (The probability that Jen will visit Madagascar and not Chile) = The probability that Jen will visit Chile*The probability that Jen will NOT visit Madagascar + The probability that Jen will visit Madagascar * The probability that Jen will NOT visit Chile = 50%*75% + 25%*50% = 50%

IMO B
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