Therese Felser manages a grocery warehouse which encourages volume shopping on the part of its customers. Therese has discovered that, on any given weekday 70 percent of the customer sales amount to more than $ 100. That is any given sale on such a day has a probability of 0.70 of being for more than $ 100.( Actually the conditional probabilities throughout the day would change slightly, depending on earlier sales, but this effect would be negligible for the first several sales of the day, so we can treat them as independent.)

Question

Therese Felser manages a grocery warehouse which encourages volume shopping on the part of its customers. Therese has discovered that, on any given weekday 70 percent of the customer sales amount to more than $ 100. That is any given sale on such a day has a probability of 0.70 of being for more than $ 100.( Actually the conditional probabilities throughout the day would change slightly, depending on earlier sales, but this effect would be negligible for the first several sales of the day, so we can treat them as independent.)

a) The first two sales on Wednesday are both for more than $ 100.
b) None of the first three sales on Wednesday is for more than $ 100

Answer 1

a) To calculate the probability of the first two sales on Wednesday both being for more than $100, we can multiply the probability of the first sale being more than $100 by the probability of the second sale also being more than $100.

Given that any given sale on a weekday has a probability of 0.70 of being for more than $100, the probability of the first sale being more than $100 is 0.70.

Since the sales are treated as independent, the probability of the second sale also being more than $100 is also 0.70.

To calculate the probability of both events occurring, we multiply the probabilities:
0.70 * 0.70 = 0.49

Therefore, the probability of the first two sales on Wednesday both being for more than $100 is 0.49, or 49%.

b) To calculate the probability of none of the first three sales on Wednesday being for more than $100, we need to find the complement of the event "at least one sale is for more than $100".

Since the sales are treated as independent, the probability of a sale being for more than $100 is 0.70. Therefore, the probability of a sale being for less than or equal to $100 is 1 - 0.70 = 0.30.

To calculate the probability of none of the first three sales being for more than $100, we multiply the probabilities of each sale being for less than or equal to $100:
0.30 * 0.30 * 0.30 = 0.027

Therefore, the probability of none of the first three sales on Wednesday being for more than $100 is 0.027, or 2.7%.