Question

a dentist polls his patients and finds that 83 percent brush their teeth at least twice a day, 47 percent floss daily, and 19 percent brush at least twice a day and floss daily. what is the probability that a patient flosses daily, given that he or she brushes at least twice a day? round to the nearest percent. 16% 23% 40% 57%

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( A \) is the event of flossing daily and \( B \) is the event of brushing at least twice a day.

Step2: Identify Given Probabilities

We know \( P(B) = 0.83 \) (83% brush at least twice a day), \( P(A \cap B) = 0.19 \) (19% do both).

Step3: Calculate Conditional Probability

Substitute into the formula: \( P(A|B) = \frac{0.19}{0.83} \approx 0.2289 \), which rounds to 23%.

Answer:

23% (corresponding to the option with "23%")