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%

Answer 1

The E2020 answer is 23 percent

Answer 2

Answer:

The correct option is B. 23%

Step-by-step explanation:

Let the event that patient brushes his teeth at least twice a day is denoted by A

So, P(A) = 0.83

Let the event that patient flosses daily is denoted by B

So, P(B) = 0.47

Now, it is given that 19 percent patients brush at least twice a day and floss daily.

⇒ P(A and B) = 0.19

Now, we need to find conditional probability of occurring event B given A has occurred.

$\implies P(B|A) =\frac{P(A\: and\: B)}{P(A)}\\\\\implies P(B|A) = \frac{0.19}{0.83}\\\\\implies P(B|A) = 0.2289\approx 0.23$

Hence, Nearest required percentage = 23%

Therefore, The correct option is B. 23%