{"id":57132,"date":"2024-04-16T00:56:45","date_gmt":"2024-04-16T00:56:45","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=57132"},"modified":"2024-04-16T00:56:45","modified_gmt":"2024-04-16T00:56:45","slug":"the-probability-that-a-person-owns-a-sports-car-given-that-they-subscribe-to-automotive-magazine-is-40-we-also-know-that-3-of-the-adult-population-subscribes-to-automotive-magazine-the-probability-o","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-probability-that-a-person-owns-a-sports-car-given-that-they-subscribe-to-automotive-magazine-is-40-we-also-know-that-3-of-the-adult-population-subscribes-to-automotive-magazine-the-probability-o\/","title":{"rendered":"The probability that a person owns a sports car given that they subscribe to automotive magazine is 40%. We also know that 3% of the adult population subscribes to automotive magazine. The probability of a person owning a sports car given that they don’t subscribe to automotive magazine is 30%. Use this information to compute the probability that a person subscribes to automotive magazine given that they own a sports car"},"content":{"rendered":"

[amp_mcq option1=”0.0398″ option2=”0.0389″ option3=”0.0368″ option4=”0.0396″ correct=”option4″]<\/p>\n

The correct answer is $\\boxed{\\text{B. }0.0389}$.<\/p>\n

The probability that a person subscribes to automotive magazine given that they own a sports car is denoted by $P(S|C)$. We can calculate this probability using Bayes’ theorem:<\/p>\n

$$P(S|C) = \\frac{P(C|S)P(S)}{P(C)}$$<\/p>\n

We are given that $P(C|S) = 0.4$, $P(S) = 0.03$, and $P(C) = 0.03 + 0.3 = 0.33$. Substituting these values into Bayes’ theorem, we get:<\/p>\n

$$P(S|C) = \\frac{(0.4)(0.03)}{(0.33)} = 0.0389$$<\/p>\n

Therefore, the probability that a person subscribes to automotive magazine given that they own a sports car is $\\boxed{\\text{B. }0.0389}$.<\/p>\n

Here is a brief explanation of each option:<\/p>\n