Question

A sales man knows that, on each visit to a customer, the probability of a sale is one fifth. Each day he makes three independent visits to customers.
Calculate the probability that, on a randomly selected day:
(a) all three visits result in sales. (5 marks)
(b) exactly two visits results in sales. (5 marks)
(c) less than two visits results in sales

Answer 1

Answer on Question#54699 - Math - Statistics and Probability

A sales man knows that, on each visit to a customer, the probability of a sale is one fifth. Each day he makes three independent visits to customers.

Calculate the probability that, on a randomly selected day:

(a) all three visits result in sales. (5 marks)

(b) exactly two visits results in sales. (5 marks)

(c) less than two visits results in sales

Solution:

(a) Since the probability of a sale is $\frac{1}{5}$, the probability of all three visits result in sales is:

$$\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} = \frac{1}{125} = 0.008$$

(b) Since the probability of a sale to fail is $\frac{4}{5}$, the probability of exactly two visits results in sales is:

$$\frac{4}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} = \frac{4}{125} = 0.032$$

(c) Less than two means one visit, therefore other two result in fail. The probability of such case is:

$$\frac{1}{5} \cdot \frac{4}{5} \cdot \frac{4}{5} = \frac{16}{125} = 0.128$$

Answer:

(a) 0.008

(b) 0.032

(c) 0.128

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