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 $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that a patient flosses daily and $B$ be the event that a patient brushes their teeth at least twice a day. We are given that $P(B) = 0.83$, $P(A\cap B)=0.19$.

Step2: Substitute values into the formula

Substitute $P(A\cap B) = 0.19$ and $P(B)=0.83$ into the formula $P(A|B)=\frac{P(A\cap B)}{P(B)}$. So $P(A|B)=\frac{0.19}{0.83}$.

Step3: Calculate the probability

$P(A|B)=\frac{0.19}{0.83}\approx0.23$. Convert this decimal to a percentage: $0.23\times100 = 23\%$.

Answer:

23%