Statistics probability

Question

If it rains 10% of the time in Phoenix Arizona and I go there for 14 days what is the probability that it will rain:

A. One day?

b. More than 2 days?

c. Four or more days?

d. Not at all?

e. Less than five days?

f. How many days should I expect it to rain?

Answer 1

use binomial distribution

x = number of days it will rain

p = 0.1 = probability of rain

n = number of days = 14

P(x = k), where k = number of days of rain = C(n,k) p^k * (1-p)^(n-k)

A. One day?

k = 1



b. More than 2 days?

same as 1 - probability two or less days

compute probability for k = 0, 1 and 2, sum probabilities, then subtract from 1

c. Four or more days?

same as 1 - probability three or less days

compute probability for k = 0, 1, 2 and 3, sum probabilities, then subtract from 1

d. Not at all?

k = 0

e. Less than five days?

compute probability for k = 0, 1, 2, 3 and 4, sum probabilities

f. How many days should I expect it to rain?

n*p = 14 * 0.1 = 1.4 days