Question

A local downtown arts and crafts shop found from past observation that 15% of the people who enter the shop actually buy something. Three potential customers enter the shop.

a. How many outcomes are possible for whether the clerk makes a sale to each customer? Construct a tree diagram to show the possible outcomes. Let Y=sale, N=no sale.



b. Find the probability of making at least one sale to the 3 customers.

Answer 1

Answer:

a. Please refer to the diagram below

b. 0.385875

Step-by-step explanation:

The tree diagram is shown below.

To calculate the probability of at least one sale to the three customers, we have to ways. The easier way is to calculate the probability of no sales to three and subtract the value from one:

$1-0.614125=0.385875$

Other way is to calculate the sum of following probabilities:

One sale + Two sale + Three sale.

$0.003375+0.019125+0.019125+0.108375+0.019125+0.108375+0.108375=0.385875$

For the probability, please refer to the tree diagram. If moving to the sub branch of the previous branch, we multiply the probability; otherwise we add.