Question

A typical dinne or a family of four, has 7 components- bread, soup, salad, fries, protein, dessert, drink. Each component is 99% good. Find the following: Probability (single meal for one person is good)- Probability (one dinner for all the family members is good)- Probability (all dinners for the whole month of 30 days are good)- . Probability (all dinners for the whole year of 12 months are good)- Quality of each dinner component was improved to 99.9% good. Calculate the following probabilities again. .Probability (single meal for one person is good) - Probability (one dinner for all the family members is good)- Probability (all dinners for the whole month of 30 days are good)- Probability (all dinners for the whole year of 12 months are good) -

Answer 1

This is a binomial distribution question with
n = 7
p = 0.99
q = 1 - p = 0.01
where
$P(X = x) = \binom{n}{x} p^x q^{n-x}$
x = 7
$P(X = 7) = \binom{7}{7} 0.99^{7} 0.01^{7-7}$
P(single mean for one person is good) = 0.9321
P(one dinner for all family member be good) = P(single mean for one person is good)⁴

P(one dinner for all family member be good) = 0.9321⁴ = 0.7548

P(all dinner for whole month of 30 days are good) = P(one dinner for all family member be good)³⁰

P(all dinner for whole month of 30 days are good) = 0.7548³⁰ = 0.0002165

P(all dinner for whole years of 12 months are good) = P(all dinner for whole month of 30 days are good)¹²

P(all dinner for whole years of 12 months are good) = 0.0002165¹² = 1.0617 * 10^-44

This is a binomial distribution question with
n = 7
p = 0.999
q = 1 - p = 0.01
where
$P(X = x) = \binom{n}{x} p^x q^{n-x}$
x = 7
$P(X = 7) = \binom{7}{7} 0.999^{7} 0.001^{7-7}$
P(single mean for one person is good) = 0.993
P(one dinner for all family member be good) = P(single mean for one person is good)⁴

P(one dinner for all family member be good) = 0.993⁴ = 0.9723

P(all dinner for whole month of 30 days are good) = P(one dinner for all family member be good)³⁰

P(all dinner for whole month of 30 days are good) = 0.9723³⁰ = 0.43043

P(all dinner for whole years of 12 months are good) = P(all dinner for whole month of 30 days are good)¹²

P(all dinner for whole years of 12 months are good) = 0.43043¹² = 4.045 * 10^-5