using bayes theorem, what would be the probability of a honda civic being stolen 53% of civics are stolen and 46% were other honda cars
To calculate the probability of a Honda Civic being stolen using Bayes' theorem, we need to know the following probabilities:
P(Stolen) - the probability of any car being stolen
P(Civic) - the probability of a randomly chosen car being a Honda Civic
P(Other Honda) - the probability of a randomly chosen car being another type of Honda car (besides Civic)
Based on the information given, we have the following probabilities:
P(Stolen) = 53%
P(Civic) = ?
P(Other Honda) = 46%
To find P(Civic), we subtract P(Other Honda) from 100% because the sum of the probabilities of all Honda cars (including Civic and Other Honda) should equal 100%. So, P(Civic) = 100% - P(Other Honda) = 100% - 46% = 54%.
Now, we can use Bayes' theorem:
P(Stolen|Civic) = (P(Civic|Stolen) * P(Stolen)) / P(Civic)
P(Civic|Stolen) is the probability of a Honda Civic being stolen, which is not given directly. However, we can assume that if 53% of cars are stolen, and Honda Civics make up 54% of cars, then the percentage of stolen cars that are Honda Civics would be approximately 53% * (54% / 100%) = 28.62%.
Therefore, we can calculate the probability of a Honda Civic being stolen using Bayes' theorem:
P(Stolen|Civic) = (28.62% * 53%) / 54% = 0.2775 or approximately 27.75%
So, the probability of a Honda Civic being stolen is approximately 27.75%.