Probability (maths)

yer_averagejoe · 10 Mar 2006 at 02:13

can someone help me with this please?

If on average rain falls 12 days out of every 30, find the probability that rain will fall 3 days in one week.

The answer I keep getting is close, but its definetl no cigar.

cheers, Joe

daz · 10 Mar 2006 at 02:23

What have you done so far?

King4aDay · 10 Mar 2006 at 02:25

ignore

yer_averagejoe · 10 Mar 2006 at 02:36

well so far Im using the formula:

prob. of rain on 3 out of 7 days = (e^(-u) * r^u)/r!

where u = np = 7[7days] * (12/30)

so u = 0.4*7 = 2.8

and r = number of rainy days = 3

i keep getting an answer of 0.22 when the answer should be 0.29

Joe

Seft · 10 Mar 2006 at 02:44

I've forgotton a lot of my stats, but it looks to me like you're using a Poisson approximation (which won't be so great as n is relatively small).

The exact binomial method would be:

P = probability of k
n = number of tries
k = desired outcome
p = probability of single occurrence
q = 1 - p

P = (n!/k!(n-k)!)(p^k)(q^(n-k))

P = (7!/3!(7-3)!)(0.4^3)(0.6^(7-3)) should give you 0.29

yer_averagejoe · 10 Mar 2006 at 02:58

ahh cheers, yeah i was using the wrong method.