The probability of rain on each of five days is 1/6, except on the fir

Question

The probability of rain on each of five days is 1/6, except on the first day, when it is 2/5, and on the last day, when it is 4/5. What is the probability that rain will occur on at least one of the five days?

(A) 1/675
(B) 5/72
(C) 5/27
(D) 22/27
(E) 67/72

(A) 1/675 
(B) 5/72 
(C) 5/27 
(D) 22/27 
(E) 67/72

Luckisnoexcuse · Accepted Answer

No rain on all days
 3/5*5/6*5/6*5/6*1/5 = 15/216

Atleast 1 day rain =  1-15/216 = 201/216 = 67/72

pushpitkc · Answer

Given data : 
Probability of raining on 1st day =  \frac{2}{5} 
Probability of raining on other days =  \frac{1}{6} 
Probability of raining on 5th day =  \frac{4}{5}

From this we can find probability it didn't rain on 
Day 1 = 1 -  \frac{2}{5}  =  \frac{3}{5} 
Day 2,3,4 = 1 -  \frac{1}{6}  =  \frac{5}{6} 
Day 5 = 1 -  \frac{4}{5}  =  \frac{1}{5}

Since we have been asked to find the probability of rain on at least 1 days,
the easiest was is to find the probability that it doesn't rain on either of the days.

P(Raining on at least one day) = 1 - P(Not raining on single day)
= 1 - ( \frac{3}{5}*\frac{5}{6}*\frac{5}{6}*\frac{5}{6}*\frac{1}{5} ) = 1 -  \frac{5}{72} = \frac{67}{72}  (Option E)

TimeTraveller · Answer

Probability of rain on at least one of the days = 1 - (Probability of rain on no day).

Probability of rain on Day-1 =  \frac{2}{5} , no rain =  \frac{3}{5} .
Probability of rain on Day-2 = Day-3 = Day-4 =  \frac{1}{6} , no rain =  \frac{5}{6} .
Probability of rain on Day-4 =  \frac{4}{5} , no rain =  \frac{1}{5} .

Probability of rain on at least one of the days =  1 - (\frac{3}{5} * (\frac{5}{6})^{3} * \frac{1}{5}) = 1 - \frac{15}{216} = 1 - \frac{5}{72} = \frac{67}{72} . Ans - E.

GTExl · Answer

Probability that rain will not happen on any day is-

=(1-2/5)(1-1/6)(1-1/6)(1-1/6)(1-4/5)
=3/5*5/6*5/6*5/6*1/5
=5/72

now for probability of rain to occur on at least one of five days, We will subtract probability of not occurring into 1 i.e

=1-5/72
=67/72

Answer is E

alen123 · Answer

What if it was asked to find the probability of raining for atleast 2 days??

Sent from my Redmi Note 4 using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

Solution:
 
The probability that it will rain on at least one of the five days is 1 minus the probability that it will not rain on any of the five days. The probability that it will not rain on any of the five days is 3/5 x 5/6 x 5/6 x 5/6 x 1/5 = (3 x 5)/(6 x 6 x 6) = 5/(2 x 6 x 6) = 5/72. Therefore, the probability that it will rain on at least one of the five days is 1 - 5/72 = 67/72

Answer: E

MathRevolution · Answer

Probability of at least 1-day rain: 1 - (No rain on any day)

Probability of rain on first day :  \frac{2 }{ 5}  ; hence probability of no rain on first day : 1 -  \frac{2 }{ 5}  =  \frac{3 }{ 5}

Probability of rain on second, third and fourth day (each) :  \frac{1 }{ 6}  ; hence probability of no rain on each day : 1 -  \frac{1 }{ 6}  =  \frac{5 }{ 6}

Probability of rain on last day :  \frac{4 }{ 5}  ; hence probability of no rain on last day : 1 -  \frac{4 }{ 5}  =  \frac{1 }{ 5}

Overall Probability of at least 1-day rain: 1 -(  \frac{3 }{ 5} * \frac{5 }{ 6} * \frac{5 }{ 6} * \frac{5 }{ 6} * \frac{1 }{ 5} )

=> 1 -  \frac{5 }{ 72}

=>  \frac{67 }{ 72}

Answer E

shreyasaxena2301 · Answer

Can someone explain concept behind- at least - questions..also is there any post where I can get all probability concepts and formulas..thanks in advance.

Posted from my mobile device

Abhishek009 · Answer

Find here - https://gmatclub.com/forum/math-probability-87244.html

bumpbot · Answer

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The probability of rain on each of five days is 1/6, except on the fir

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