a dentist was making note of her upcoming appointments with different aged patients and the reasons for…

a dentist was making note of her upcoming appointments with different aged patients and the reasons for their visits.\n| |regular cleaning|broken tooth|\n|--|--|--|\n|patients under 18|5|3|\n|patients 19 - 60|2|3|\n|patients over 60|4|4|\nwhat is the probability that a randomly selected appointment is for a regular cleaning given that the appointment is with a patient 19 - 60?\nsimplify any fractions.

a dentist was making note of her upcoming appointments with different aged patients and the reasons for their visits.\n| |regular cleaning|broken tooth|\n|--|--|--|\n|patients under 18|5|3|\n|patients 19 - 60|2|3|\n|patients over 60|4|4|\nwhat is the probability that a randomly selected appointment is for a regular cleaning given that the appointment is with a patient 19 - 60?\nsimplify any fractions.

Answer

Explanation:

Step1: Find total appointments for 19 - 60 patients

Add the number of regular - cleaning and broken - tooth appointments for patients 19 - 60. $2 + 3=5$

Step2: Find number of regular - cleaning appointments for 19 - 60 patients

The number of regular - cleaning appointments for patients 19 - 60 is 2.

Step3: Calculate the conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In this case, the probability that an appointment is for a regular cleaning given that the patient is 19 - 60 is the number of regular - cleaning appointments for 19 - 60 patients divided by the total number of appointments for 19 - 60 patients. So the probability is $\frac{2}{5}$.

Answer:

$\frac{2}{5}$