Question

At a dental office, the probability a patient needs a cleaning is 0.89. The probability a patient

needs a filling is 0.44. Assuming the events "needs a cleaning" and "needs a filling" are
independent, then what is the probability a patient needs a filling given that he/she needs a cleaning?
A. 0.83
B. Additional information is required to determine the probability.
C.0.39
D. 0.89
E. 0.44

Answer 1

Answer: 0.44

Reason:

The events "needs a cleaning" and "needs a filling" are independent. Therefore, we can immediately conclude that the prior condition "needs a cleaning" does not affect "needs a filling". That's why we go for the answer of 0.44 which is stated in the instructions.

In terms of symbols:

• C = patient needs a cleaning
• F = patient needs a filling
• P(C) = 0.89 = probability the patient needs a cleaning
• P(F) = 0.44
• P(F given C) = P(F) .... since F and C are independent
• P(F given C) = 0.44

The knowledge about event C happening does not change the value of P(F). Now if events F and C were dependent somehow, then P(F given C) would be different from P(F).