Final answer:
To calculate the probability, we can use Bayes' Theorem. Substituting the known values into the equation, we can determine the likelihood that a randomly selected purchaser with an extended warranty has a basic model. However, we would need the exact values of P(B) and P(D) to calculate the probability.
Step-by-step explanation:
To determine the likelihood that a randomly selected purchaser with an extended warranty has a basic model, we need to use conditional probability. We can use Bayes' Theorem to calculate the probability.
Let's define the following probabilities:
- P(B) = Probability of buying a basic model
- P(D) = Probability of buying a deluxe model
- P(E|B) = Probability of buying an extended warranty given that a basic model was purchased
- P(E|D) = Probability of buying an extended warranty given that a deluxe model was purchased
We are given that 37% of those buying the basic model purchase an extended warranty, which translates to P(E|B) = 0.37. We are also given that 46% of all deluxe purchasers purchase an extended warranty, which translates to P(E|D) = 0.46.
Now, we need to calculate P(B|E), which is the probability of having a basic model given that an extended warranty was purchased.
Using Bayes' Theorem, we have:
P(B|E) = (P(E|B) * P(B)) / (P(E|B) * P(B) + P(E|D) * P(D))
Substituting the known values, we get:
P(B|E) = (0.37 * P(B)) / (0.37 * P(B) + 0.46 * P(D))
Since we don't have the exact values for P(B) and P(D), we cannot calculate the exact probability. However, we can use the given information that 497 cameras sold were of the basic model. We can assume that P(B) = 497 / (497 + P(D)) and solve for P(B|E) using this equation.
Finally, we can substitute the value of P(B|E) to calculate the probability.