Question

Suppose 30% of business majors major in accounting. You take a random sample of 3 business majors. Answer questions 39 and 40: What is the chance that at least one student majors in accounting?

Answer 1

The chance that at least one student out of three business majors is an accounting major is 65.7%.

Step-by-step explanation:

The question asks: What is the chance that at least one student majors in accounting? To answer this question, we will use the complement rule. The complement of at least one student majoring in accounting is that no student majors in accounting. Since 30% of business majors are in accounting, there is a 70% chance a randomly selected business major is not an accounting major. For three independent selections, the probability that all three students are not accounting majors is (0.70)^3, which equals 0.343.

To find the probability of at least one accounting major, you subtract this value from 1. So, the chance that at least one student majors in accounting is 1 - 0.343, which equals 0.657 or 65.7%.

This is calculated as follows:

• Probability of no accounting majors: 0.70 x 0.70 x 0.70 = 0.343
• Probability of at least one accounting major: 1 - 0.343 = 0.657

Answer 2

The probability that at least one student majors in accounting=0.3×0.3×0.3=0.027

Step-by-step explanation:

Step 1: Determine the number of accounting majors in a business

N=P×S

where;

N=number of accounting majors

P=probability of accounting majors

S=sample size

This can also be written as;

Number of accounting majors=probability of accounting majors×sample size

In our case;

Number of accounting majors=unknown, to be determined

Probability of accounting majors=30%=30/100=0.3

Sample size=3 business majors

Substituting;

Number of accounting majors=0.3×3=0.9

Step 2: Determine the chance that at least one student majors in accounting

The probability that at least one student majors in accounting=0.3×0.3×0.3=0.027