Question

On average, my family eats chocolate 4 times each week. The probability of us eating chocolate is the same for any fixed length of time, and eating chocolate at any point does not impact the odds of us eating chocolate at another point. (Our chocolate consumption is independent.)

a. What is the probability that we eat chocolate 4 times in one week?

b. What is the probability that we eat chocolate twice or fewer in one week?

c. What is the probability that we eat chocolate once on any given day?

d. Assume that we could only eat chocolate once on a given day or not at all. Given this restriction, what is the probability that we would eat chocolate?

e. How do answers (c) and (d) compare with one another?

Answer 1

Let X denotes the number of chocolates one can eat in a randomly selected week.

X ~ Poisson(4)

The probability mass function of X is

a) The probability that we eat chocolate 4 times in one week

b) The probability that we eat chocolate twice or fewer in one week

c) Let Y denotes the number of chocolates one can eat in a randomly selected day.

Y ~ Poisson(4/7) or Y ~ Poisson(0.5714)

The probability mass function of Y is

The probability that we eat chocolate once on any given day

d) The probability that we would eat chocolate

= P( we eat chocolate once on any given day )

e) answers of (c) and (d) are same.