2. Tristan and Laura were investigating ancient Voodoo beliefs of Mount Hope and Ancaster. In ancient times, the villagers believed that the Voodoo Gods must be happy to have a successful harvest each year. If the probability that the Voodoo Gods would be happy was ,
a) Show the binomial probability distribution that there would be a successful harvest four years in a row. [5]

b) What is the probability the Voodoo Gods will be happy for at least two of the four years? [2]

Question

2.  Tristan and Laura were investigating ancient Voodoo beliefs of Mount Hope and Ancaster.  In ancient times, the villagers believed that the Voodoo Gods must be happy to have a successful harvest each year.  If the probability that the Voodoo Gods would be happy was   ,
a)  Show the binomial probability distribution that there would be a successful harvest four years in a row. [5]

b)  What is the probability the Voodoo Gods will be happy for at least two of the four years? [2]

daenio · Answer

@jim_thompson5910 @satellite73  @LagrangeSon678 @Mertsj  @kropot72 @UnkleRhaukus  @radar  @Chlorophyll

jim_thompson5910 · Answer

You're missing the probability

daenio · Answer

Tristan and Laura were investigating ancient Voodoo beliefs of Mount Hope and Ancaster.  In ancient times, the villagers believed that the Voodoo Gods must be happy to have a successful harvest each year.  If the probability that the Voodoo Gods would be happy was 1/5,
a)  Show the binomial probability distribution that there would be a successful harvest four years in a row. [5]

Sorry about that! @jim_thompson5910

jim_thompson5910 · Answer

a)

If you're only taking 4 years into account and that's it, then the probability is simply (1/5)^4 = 1/625 = 0.0016

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b)

P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 2) = (4 C 2)*(0.2)^(2)*(1-0.2)^(4-2)

P(X = 2) = (4 C 2)*(0.2)^(2)*(0.8)^(4-2)

P(X = 2) = (6)*(0.2)^(2)*(0.8)^2

P(X = 2) = (6)*(0.04)*(0.64)

P(X = 2) = 0.1536


P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 3) = (4 C 3)*(0.2)^(3)*(1-0.2)^(4-3)

P(X = 3) = (4 C 3)*(0.2)^(3)*(0.8)^(4-3)

P(X = 3) = (4)*(0.2)^(3)*(0.8)^1

P(X = 3) = (4)*(0.008)*(0.8)

P(X = 3) = 0.0256


P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 4) = (4 C 4)*(0.2)^(4)*(1-0.2)^(4-4)

P(X = 4) = (4 C 4)*(0.2)^(4)*(0.8)^(4-4)

P(X = 4) = (1)*(0.2)^(4)*(0.8)^0

P(X = 4) = (1)*(0.0016)*(1)

P(X = 4) = 0.0016


So 

P(X >= 2) = 0.1536+0.0256+0.0016

P(X >= 2) = 0.1808


which means that the probability the Voodoo Gods will be happy for at least two of the four years is 0.1808

daenio · Answer

Wow man. I didn't think it involved that much work. Thank you very much for taking the time for a detailed answer! :)

jim_thompson5910 · Answer

you're welcome