Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities. assume the probability that you will make a sale on any given telephone call is 0.18. find the probability that you (a) make your first sale on the fifth call, (b) make your first sale on the first, second, or third call, and (c) do not make a sale on the first three calls. (a) p(make your first sale on the fifth call) = 0.081 (round to three decimal places as needed.) (b) p(make your first sale on the first, second, or third call) = 0.449 (round to three decimal places as needed.) (c) p(do not make a sale on the first three calls) = \square (round to three decimal places as needed.)

Explanation:

Step1: Identify the probability of not making a sale

The probability of making a sale on a given call is \( p = 0.18 \), so the probability of not making a sale on a single call is \( q = 1 - p = 1 - 0.18 = 0.82 \).

Step2: Calculate the probability of not making a sale on the first three calls

Since the calls are independent events, the probability of not making a sale on the first, second, and third calls is the product of the probabilities of not making a sale on each individual call. Using the multiplication rule for independent events, we have:

$$ P(\text{do not make a sale on the first three calls}) = q \times q \times q = q^3 $$

Substituting \( q = 0.82 \) into the formula:

$$ P = 0.82^3 $$

Calculating \( 0.82^3 \):

$$ 0.82 \times 0.82 = 0.6724 $$

$$ 0.6724 \times 0.82 = 0.551368 $$

Rounding to three decimal places, we get \( 0.551 \).

Answer:

\( 0.551 \)