Question

I eat potatoes often. On average, I eat potatoes 4 times per week. The probability of me eating a potato is the same for any fixed length of time, and eating a potato at any point does not impact the odds of me eating a potato at another point, i.e. independent eatings.

1) What is the probability I eat a potato once on any given day?

2) Assume that I could only eat a potato once on a given day or not at all. Given this restriction, what is the probability that I eat a potato?

3) How do the the answers to 1 and 2 compare?

Answer 1

1) here this will follow Poisson distribution with parameter =4/7 =average potato eaten in a day,

hence probability I eat a potato once on any given day =P(X=1)=e^-4/7*(4/7)¹/1! =0.322696

2) here as there are total on average eaten potatoes are 4 ; therefore probability that I eat a potato on a given day =0.571429

3) probability in part 2 is higher then in part 1.