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Retired Moderator
Joined: 16 Apr 2020
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The probability of rain on any given day in a particular city is 50%.
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13 Aug 2021, 08:28
13 Aug 2021, 08:28
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The probability of rain on any given day in a particular city is 50%.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Probability that it will rain on at least three days in a row during a five-day period |
\(\frac{3}{16}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Intern
Joined: 25 Oct 2020
Posts: 20
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Location: India
Concentration: Strategy, Finance
Re: The probability of rain on any given day in a particular city is 50%.
[#permalink]
13 Aug 2021, 21:53
13 Aug 2021, 21:53
2
There are 8 cases in which it will rain for at least three days in a row.
Rain-Rain-Rain-Rain-Rain
Rain-Rain-Rain-rain-no rain
no rain-rain-rain-rain-rain
rain-rain-rain-no rain no rain
no rain-no rain-rain-rain-rain
rain-rain-rain-no rain-rain
rain-no rain-rain-rain-no rain
no rain- rain-rain-rain-no rain
Given that the probability to rain on any given day is 50% or 1/2
So the probability for each of the case will be (1/2) raised to the power 5 which is 1/16
and 8 cases so 8*(1/16)=8/16
which is greater than 3/16, So the answer is A
Rain-Rain-Rain-Rain-Rain
Rain-Rain-Rain-rain-no rain
no rain-rain-rain-rain-rain
rain-rain-rain-no rain no rain
no rain-no rain-rain-rain-rain
rain-rain-rain-no rain-rain
rain-no rain-rain-rain-no rain
no rain- rain-rain-rain-no rain
Given that the probability to rain on any given day is 50% or 1/2
So the probability for each of the case will be (1/2) raised to the power 5 which is 1/16
and 8 cases so 8*(1/16)=8/16
which is greater than 3/16, So the answer is A
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: The probability of rain on any given day in a particular city is 50%.
[#permalink]
14 Aug 2021, 06:01
14 Aug 2021, 06:01
2
nikhilinuganti wrote:
There are 8 cases in which it will rain for at least three days in a row.
Rain-Rain-Rain-Rain-Rain
Rain-Rain-Rain-rain-no rain
no rain-rain-rain-rain-rain
rain-rain-rain-no rain no rain
no rain-no rain-rain-rain-rain
rain-rain-rain-no rain-rain
rain-no rain-rain-rain-no rain
no rain- rain-rain-rain-no rain
Given that the probability to rain on any given day is 50% or 1/2
So the probability for each of the case will be (1/2) raised to the power 5 which is 1/16
and 8 cases so 8*(1/16)=8/16
which is greater than 3/16, So the answer is A
Rain-Rain-Rain-Rain-Rain
Rain-Rain-Rain-rain-no rain
no rain-rain-rain-rain-rain
rain-rain-rain-no rain no rain
no rain-no rain-rain-rain-rain
rain-rain-rain-no rain-rain
rain-no rain-rain-rain-no rain
no rain- rain-rain-rain-no rain
Given that the probability to rain on any given day is 50% or 1/2
So the probability for each of the case will be (1/2) raised to the power 5 which is 1/16
and 8 cases so 8*(1/16)=8/16
which is greater than 3/16, So the answer is A
Great work but the marked part would be \(\frac{1}{32}\)
So, the answer would be \(\frac{1}{4}\)
