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. 23% 57% 16% 40%

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: Substitute the given values into the formula

We are given that \(P(B) = 0.83\) (83% in decimal form) and \(P(A\cap B)=0.19\) (19% in decimal form).
So, \(P(A|B)=\frac{0.19}{0.83}\).

Step3: Calculate the value

\(\frac{0.19}{0.83}\approx0.2289\).

Step4: Convert to percentage and round

\(0.2289\times100 = 22.89\%\approx23\%\).

Answer:

23%