Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60587

A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
17 Apr 2018, 05:22
Question Stats:
45% (01:55) correct 55% (01:34) wrong based on 147 sessions
HideShow timer Statistics
A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled? A. 40% B. 49% C. 55% D. 66% E. 75%
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Manager
Joined: 30 May 2017
Posts: 137
Location: United States
GPA: 3.57

A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
17 Apr 2018, 05:49
Bunuel wrote: A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled?
A. 40% B. 49% C. 55% D. 66% E. 75% Probability of temp at or above 20 degrees = 100%15% = 85% The likelihood that the trip will NOT be cancelled = prob of temp at or above 20 degrees * prob that it will not snow = 85% * 60% = 51% The likelihood that the trip will be cancelled = 100%  The likelihood that the trip will NOT be cancelled = 100% 51% = 49% Hence option B = 49% is the answer.




Manager
Joined: 14 Sep 2016
Posts: 59
Concentration: Finance, Economics

A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
Updated on: 27 Apr 2018, 12:16
P(A) Cold = 15% P(B) Snow = 40%
P(AuB) = 55% Snow and cold are not mutually exclusive. It can be too cold and snow simultaneously. Remove this overlap P(AnB) = During the 40% chance of snow, 15% of the time it will be under 20 degrees. Remove 15% of 40% or 6%. (.15 * .4 = .06) P(AuB) = P(A) + P(B)  (AnB) = 49% chance of cancellation
Although I don't like this problem, it's unrealistic. If it's already going to snow, if that 40% is going to happen then the 15% chance of cold has already drastically improved its chances. That 15% cold probability is taking into account whatever the entire forecast is that day lets say the 15% chance is based on reports that it could be anywhere from 15 degrees to 40 degrees. If the 40% snow is going to happen then its automatically under 32 degrees and the chance of cold has shifted from 15% to 48% chance.
You would need to limit the problem by saying its automatically cold enough to snow and that rain isn't an option. Same thing the other way around if its already the 15% cold hasn't the snow changes improved? Was the likelihood of the 40% weather snow forecast contingent on it being cold enough (100% chance of snow or rain, X% chance of too cold) or climate weather (x% chance of snow or rain, 100% chance of too cold)
Originally posted by IdiomSavant on 19 Apr 2018, 10:11.
Last edited by IdiomSavant on 27 Apr 2018, 12:16, edited 1 time in total.



Intern
Joined: 21 Jan 2018
Posts: 49
Location: India
GPA: 2.85
WE: Consulting (Consulting)

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
22 Apr 2018, 00:45
pikolo2510 wrote: Hey Bunuel / JeffTargetTestPrepNeed your help with the below approach P(temp < 20) = P(A) P(snow) = P(B) P(A) = 15% P(B) = 60% P(A n B) = 15% x 60% = 9% The probability of trip being cancelled = P(A) + P(B)  P(A n B) = 15% + 60%  9% = 66% Can you let me know what is wrong in my approach Nothing wrong with the approach, just that 60% is the P(No Snow). So in your calculations P(B) has to be 40% P(A n B ) = 6% P (Trip cancelled) = 55/100  6/100 P(Trip Cancelled) = 49%



Manager
Status: The darker the night, the nearer the dawn!
Joined: 16 Jun 2018
Posts: 182
GMAT 1: 640 Q50 V25

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
21 Jul 2018, 06:52
renjana wrote: A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled?
A. 40% B. 49% C. 55% D. 66% E. 75%
P(Trip cancelled )= P(Temp less than 20) +(OR) P(Snowing)
(P(Temp less than 20) = 15/100
P(Snowing) = 40/100
P(Trip cancelled )= 55/100
Please correct me if i am wrong ! The question is looking for the likelihood in which the trip will be canceled. A: Temp less than 20 = 15%B: Snowing = 40%not A: Temp not less than 20 = 85%not B: Not Snowing = 60%The occurrence of A & B are parallel and Happening of either of them will cancel the trip. The trip is going to be canceled under the following conditions: A*B + A*(not B) + (not A)*B : 15% * 40% + 15% * 60% + 85% * 40% = 49% Shortcut method: Find the probability in which trip will happen and subtract from the total set of events, i.e., 1  (when trip won't be canceled) : 1  (not A)*(not B)



Manager
Joined: 11 Jun 2015
Posts: 80
Location: India
Concentration: Marketing, Leadership

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
19 Apr 2018, 06:52
A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled?
A. 40% B. 49% C. 55% D. 66% E. 75%
P(Trip cancelled )= P(Temp less than 20) +(OR) P(Snowing)
(P(Temp less than 20) = 15/100
P(Snowing) = 40/100
P(Trip cancelled )= 55/100
Please correct me if i am wrong !



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
19 Apr 2018, 16:51
Bunuel wrote: A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled?
A. 40% B. 49% C. 55% D. 66% E. 75% We can use the equation: P(trip being canceled) = 1  P(trip not being canceled) P(trip not being canceled) = 0.85 x 0.6 = 0.51 So, P(trip being canceled) = 1  0.51 = 0.49, or 49%. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



BSchool Forum Moderator
Joined: 05 Jul 2017
Posts: 505
Location: India
GMAT 1: 700 Q49 V36
GPA: 4

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
21 Apr 2018, 04:05
Hey Bunuel / JeffTargetTestPrepNeed your help with the below approach P(temp < 20) = P(A) P(snow) = P(B) P(A) = 15% P(B) = 60% P(A n B) = 15% x 60% = 9% The probability of trip being cancelled = P(A) + P(B)  P(A n B) = 15% + 60%  9% = 66% Can you let me know what is wrong in my approach
_________________



Intern
Joined: 01 Jun 2015
Posts: 41
Location: India

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
21 Apr 2018, 05:35
P(a) + P(b)  P(aUb) = 49%



Intern
Joined: 03 Feb 2016
Posts: 11
Location: China

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
09 Aug 2018, 01:38
I think this question again reminds the fact to read the question very thoroughly..realized when i did not read through the lines and ended up messing it up. This is how i solved it (after realizing my mistake ) this could be solved using the formula P(A OR B) = P(A) + P(B)  P(A and B) Now, lets assume P(A) = T<20 degrees P(B) = snowfall (Question stem gives info of NOT snowing) So P(A) = 15/100 = 3/20 P(B) = 40/100 = 2/5 P(A OR B) = 3/20 + 2/5  (3/20*2/5)= 49/100 which is 49% So Answer = B



Manager
Joined: 02 Nov 2018
Posts: 56

Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
Show Tags
09 Dec 2019, 16:05
Bunuel wrote: A hiking club’s trip will be cancelled if, on the first day of the trip, the temperature is less than 20 degrees Fahrenheit or it is snowing. If there is a 15% chance that temperatures will be below 20 degrees and a 60% chance that it will not snow, what is the likelihood that the trip will be cancelled?
A. 40% B. 49% C. 55% D. 66% E. 75% Why is P(A & B) = P(A)*P(B)? This simplification can only be used if A and B are independent? But how do we know that is the case here?




Re: A hiking club’s trip will be cancelled if, on the first day of the tri
[#permalink]
09 Dec 2019, 16:05






