Terese manages a grocery store warehouse that encourages volume shopping on the part of customers. Therese has discovered that on any given weekday, 70% of the customers' 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.

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

a).7 x .7=0.49

b).3 x .3 x .3=0.027

a) To calculate the probability that both of the first sales on Wednesday are for more than $100, we can multiply the probabilities together.

Given that the probability of any given sale on Wednesday being for more than $100 is 0.70, we can say that the probability of the first sale being for more than $100 is 0.70.

To calculate the probability of both sales being for more than $100, we need to multiply this probability by itself:

Probability = 0.70 * 0.70 = 0.49

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

b) To calculate the probability that none of the first three sales on Wednesday are for more than $100, we can multiply the probabilities together.

Given that the probability of any given sale on Wednesday being for more than $100 is 0.70, the probability of a sale not being for more than $100 is 1 - 0.70, which equals 0.30.

To calculate the probability of none of the first three sales being for more than $100, we need to multiply this probability by itself three times:

Probability = 0.30 * 0.30 * 0.30 = 0.027

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

To find the probability for each scenario, we need to use the concept of independent events and multiply the probabilities of each individual event together.

a) The probability that the first sale on Wednesday is for more than $100 is 0.70. Since this event is independent of the second sale, the probability that the second sale is also for more than $100 is also 0.70. To find the probability that both events occur, we can multiply the probabilities together:

P(first sale > $100 on Wednesday) = 0.70
P(second sale > $100 on Wednesday) = 0.70

P(both sales > $100 on Wednesday) = P(first sale > $100 on Wednesday) * P(second sale > $100 on Wednesday) = 0.70 * 0.70 = 0.49

Therefore, the probability that the first two sales on Wednesday are both for more than $100 is 0.49.

b) The probability that the first sale on Wednesday is not for more than $100 is 1 - 0.70 = 0.30. Similarly, the probability for the second and third sales on Wednesday is also 0.30. Since each event is independent of the others, we can calculate the probability that none of the first three sales is for more than $100 by multiplying the probabilities together:

P(first sale ≤ $100 on Wednesday) = 0.30
P(second sale ≤ $100 on Wednesday) = 0.30
P(third sale ≤ $100 on Wednesday) = 0.30

P(none of the first three sales > $100 on Wednesday) = P(first sale ≤ $100 on Wednesday) * P(second sale ≤ $100 on Wednesday) * P(third sale ≤ $100 on Wednesday) = 0.30 * 0.30 * 0.30 = 0.027

Therefore, the probability that none of the first three sales on Wednesday is for more than $100 is 0.027.