Two toothpastes (A and B) are being compared for use in battling tooth decay. Pa
ID: 2927768 • Letter: T
Question
Two toothpastes (A and B) are being compared for use in battling tooth decay. Patients were randomly assigned to one of the two toothpastes. Three years later, the number of new cavities was recorded for each patient. Researchers used results of the study to construct the following probability models for the number of cavities suffered over 3 years for each toothpaste. Paste A #Cavities | 0 Probability 4 0.04 0.24 0.41 0.15 0.16 Paste B#Cavities | 0 Probability 0.12 0.40 0.48 a) (2 marks) What is the probability of having fewer than 2 cavities for each type of toothpaste? Based on the comparison of these probabilities, which toothpaste performs better? b) (2 marks) Find the expected number of cavities for each toothpaste. Based on the comparison of these expected numbers, which toothpaste performs better? c) (1 mark) Which toothpaste would you prefer to use and why?Explanation / Answer
Solution:
( a )
The probability of having fewer than 2 cavities for tootpaste A = 0.24 + 0.41 = 0.65
The probability of having fewer than 2 cavities for tootpaste B = 0.12 + 0.40= 0.52
Based on the probability of having fewer than 2 cavities, tooth paste B performs better since te probability is less than toothpaste A
( b )
the expected number of cavities for toothpaste A = ( 0 * 0.24 ) + ( 1 * 0.41 ) + ( 2 * 0.15 ) + ( 3 * 0.16 ) + ( 4 * 0.04 )
=1.33
the expected number of cavities for toothpaste B = ( 0 * 0.12 ) + ( 1 * 0.40 ) + ( 2 * 0.48 )
= 1.36
Based on the expected values , toothpaste A performs better
( C )
I prefer toothpaste A since toothpaste is less likely to get cavities
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.