Probability of Raining

[jerryragland]

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]

[iamseer]

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

[this_time_i_will]

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?

[Testluv]

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.