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Probability of Raining

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by jerryragland » Tue Apr 27, 2010 3:22 am
Source - Veritas

If the probability of rain on any given day is 50%. What is the probability that it will rain on at least 3 days in a row during a 5 day period?

Ans: [spoiler]1/4[/spoiler]
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by iamseer » Tue Apr 27, 2010 4:51 am
R = rain
N = no rain

possibilities for at least 3 consecutive days:(Rains for 5 or 4 or 3 consecutive days)
RRRRR = (1/2)^5 =1/32

NRRRR = (1/2)^5 =1/32
RRRRN = (1/2)^5 =1/32

RRRNN = (1/2)^5 =1/32
NRRRN = (1/2)^5 =1/32
NNRRR = (1/2)^5 =1/32

RRRNR = (1/2)^5 =1/32
RNRRR = (1/2)^5 =1/32

IMO answer 1/4
"Choose to chance the rapids and dance the tides"
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by this_time_i_will » Tue Apr 27, 2010 6:50 pm
iamseer wrote:R = rain
N = no rain

possibilities for at least 3 consecutive days:(Rains for 5 or 4 or 3 consecutive days)
RRRRR = (1/2)^5 =1/32

NRRRR = (1/2)^5 =1/32
RRRRN = (1/2)^5 =1/32

RRRNN = (1/2)^5 =1/32
NRRRN = (1/2)^5 =1/32
NNRRR = (1/2)^5 =1/32

RRRNR = (1/2)^5 =1/32
RNRRR = (1/2)^5 =1/32

IMO answer 1/4
Why are we counting above days marked in red as different?
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by Testluv » Tue Apr 27, 2010 10:43 pm
Why are we counting above days marked in red as different?
Because they are 2 different arrangements. If you were to write out all 32 possible arrangements, you would find that 1/4 of them (or, 8 of them as this_time_i_will showed) would have at least 3 consecutive "R"s. Those are 2.
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