Question

determining a conditional probability
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 the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Let \(A\) be the event that a patient flosses daily and \(B\) be the event that a patient brushes at least twice a day.

Step2: Identify the values

We are given that \(P(B) = 0.83\) (probability of brushing at least twice a day), \(P(A\cap B)=0.19\) (probability of brushing at least twice a day and flossing daily).

Step3: Calculate the conditional probability

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

$$P(A|B)=\frac{0.19}{0.83}\approx 0.23$$

Answer:

\(23\%\)