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 that a patient flosses daily, and \( B \) is the event that a patient brushes at least twice a day.

Step2: Identify Given Probabilities

We know that \( P(B) = 0.83 \) (83% of patients brush at least twice a day), and \( P(A \cap B) = 0.19 \) (19% of patients both brush at least twice a day and floss daily).

Step3: Calculate the Conditional Probability

Substitute the values into the formula: \( P(A|B) = \frac{0.19}{0.83} \approx 0.2289 \).

Step4: Convert to Percentage and Round

Multiply by 100 to get a percentage: \( 0.2289 \times 100 \approx 23\% \).

Answer:

23%