Question

question 30 of 50
if 15% of college students own a television, and 10% of college students own a stereo, and 2% of college students own both a television and a stereo, then the percent o
stereo is 23%.
○ false
○ true

Explanation:

Step1: Recall the principle of inclusion - exclusion for probabilities (or percentages here, since we can treat them as proportions). The formula for the percentage of students who own either a television (T) or a stereo (S) is \( P(T \cup S)=P(T)+P(S)-P(T \cap S) \). But the question is about the percentage who own a television or a stereo? Wait, no, the problem says "the percent of college students who own either a television or a stereo is 23%". Let's check: Given \( P(T) = 15\% \), \( P(S)=10\% \), \( P(T \cap S)=2\% \). Then \( P(T \cup S)=15 + 10- 2=23\% \). Wait, but the question is asking if that's correct? Wait, the problem statement: "If 15% of college students own a television, and 10% of college students own a stereo, and 2% of college students own both a television and a stereo, then the percent of college students who own either a television or a stereo is 23%." Let's apply the inclusion - exclusion principle. The formula for the number (or percentage) of elements in the union of two sets is \( n(T \cup S)=n(T)+n(S)-n(T \cap S) \). So in terms of percentage, \( P(T \cup S)=P(T)+P(S)-P(T \cap S) \). Plugging in the numbers: \( 15 + 10- 2=23 \). So the statement is True? Wait, but let's re - read. Wait, the problem is asking whether the percent who own either is 23%. So using inclusion - exclusion, yes. So the answer should be True? Wait, no, wait: Wait, the problem says "the percent of college students who own either a television or a stereo is 23%". Let's calculate: 15% own TV, 10% own stereo, 2% own both. So the number who own either is (15 - 2)+(10 - 2)+2=13 + 8+2 = 23. Or using the formula \( 15 + 10- 2=23 \). So the statement is True. Wait, but maybe I misread. Wait, the options are False or True. So according to the calculation, it's True? Wait, no, wait: Wait, 15% own TV, 10% own stereo, 2% own both. So the percentage who own either TV or stereo is 15 + 10 - 2 = 23. So the statement is True. So the answer is True? Wait, but let's check again. The inclusion - exclusion principle for two sets: \( |A \cup B|=|A|+|B|-|A \cap B| \). So in terms of percentages, it's the same. So 15 + 10 - 2 = 23. So the statement is correct, so the answer is True.

Step2: Verify the calculation. \( 15+10 = 25 \), then subtract the 2% that are counted twice (since they own both), so \( 25 - 2=23 \). So the percentage of students who own either a TV or a stereo is 23%, so the statement is True.

Answer:

True