SOLUTION: The probability of rain on a given day in September is 0.25. a) Assuming independent trials, what is the probability that there will be no rain over the three days of the Labour D

Question 909197: The probability of rain on a given day in September is 0.25.
a) Assuming independent trials, what is the probability that there will be no rain over the three days of the Labour Day Weekend?
b) Assuming independent trials, what is the probability that it will ran at least once in a given week?
c) Assuming independent trials, what is the probability that it will rain twice in one week?
d) What is the mean (i.e, expected) number of rainy days in September?
e) Is the assumption of independent trials in this example realistic?
I am still new at these concepts and am having trouble solving. Any help would be greatly appreciated.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let X~Binomial(n=3,p=.25)
a) P[X=0] = (3 choose 0)(.25)^0*(.75)^3 = .4219
Let X~Binomial(n=7, p=.25)
b) P[x>=1] = 1-P[X=0] = 1-(.75)^7 = .8665
c) P[X=2] = (7 choose 2)*(.25)^2*(.75)^5 = .3115
Let X~Binomial(n=30, p =.25) [30 days in Sept]
d) Mean of a binomial = n*p.
30 * .25 = 7.5
e) I would say that assumption of independent trials is realistic. Just cause it rains today doesn't significantly change the probability of it raining the next day as well.

RELATED QUESTIONS
Suppose it will rain on any given day eith the probability of 0.34, independent of... (answered by ilana)

On a certain day the chance of rain is 80% in San Fran and 30% in Sydney. Assume that... (answered by stanbon)

On certain day the chance of rain is 80% in San Francisco and 30% in Sydney. Assume that... (answered by alicealc)

In November, the rain in a certain valley tends to fall in storms of several days'... (answered by Boreal)

The odds of rain in June are 13:7. If rain on successive days is independent a.Find... (answered by stanbon)

The probability of rain in a certain city is 1/8 on a given day. Find the probability... (answered by rfer)

In January in a certain city the unconditional probability of rain on any given day of... (answered by stanbon)

If a sample of 50 customers is selected on a given day, assuming that the trials are... (answered by swincher4391)

Their is a 80 % chance it will rain on any given day in Seattle what is the probability... (answered by rothauserc)