Question

As an incentive to get new customers, the local branch of a bank launched 'bouncing for bucks.' During this week long event, an customer opening a new checking account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her checking account. The way the box was labeled is shown below. What is the probability that three customers in a row do not get $50? Round to three decimals.

10 30 10 30 10
20 10 50 10 20
a. 0.125

b. 0.300

c. 0.729

d. 0.970

e. 0.001

Answer 1

The probability that three customers in a row do not get $50 is 0.729 after calculating the chance of a single customer not landing on the $50 square (0.9) and raising it to the third power to account for three customers.

Step-by-step explanation:

The game described in the question involves throwing a ball into a box with squares labeled with various dollar amounts. To find the probability that three customers in a row do not get the $50 square, we need to first determine the probability of a single customer not getting the $50 square. The layout of the box is:

• 10 30 10 30 10
• 20 10 50 10 20

In total, there are 10 squares. Only one square has the $50, which means there is a 1/10 chance of landing on $50 and a 9/10 chance of not landing on it since the customer gets only one attempt. We assume each customer's throw is independent from the others so the probabilities will be multiplied for multiple customers.

The probability of one customer not getting $50 is 0.9 (9/10). To find the probability of this happening for three customers in a row, we calculate 0.93. Therefore, the final answer to the probability that three customers in a row do not get $50 is 0.93 = 0.729, rounding to three decimals.