3. (a) A city has sunny weather on 3 out of every 5 days on average....

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3. (a) A city has sunny weather on 3 out of every 5 days on average. Use the binomial formula to find the probability that exactly 4 days out of a 7 day week are sunny. Binomial formula P(x)-Cap (1-p) for x 0, 1, 2,.... n where C-n!/[x! (n-x)!] and n!-n(n-1)(n-2).... (2)(1) Note: 0! 1 P(x-4)= (b) In a certain region, there is a 1/3 probability of a hurricane occurring in a given year (i.e. an average of 1 every 3 years). Use the binomial formula to find the probability that exactly 3 hurricanes occur in the next 6 years. P(x-3)= (c) Use the Poisson formula to find the probability that at least 2 hurricanes occur in the next 8 years: P(x)-01) - x! P(x2)= 3. (a) A city has sunny weather on 3 out of every 5 days on average. Use the binomial formula to find the probability that exactly 4 days out of a 7 day week are sunny. Binomial formula P(x)-Cap (1-p) for x 0, 1, 2,.... n where C-n!/[x! (n-x)!] and n!-n(n-1)(n-2).... (2)(1) Note: 0! 1 P(x-4)= (b) In a certain region, there is a 1/3 probability of a hurricane occurring in a given year (i.e. an average of 1 every 3 years). Use the binomial formula to find the probability that exactly 3 hurricanes occur in the next 6 years. P(x-3)= (c) Use the Poisson formula to find the probability that at least 2 hurricanes occur in the next 8 years: P(x)-01) - x! P(x2)=