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 answer is B

Explanation:

Answer 2

The correct option is B. 23%

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) =(P(A\: and\: B))/(P(A))\\\\\implies P(B|A) = (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%