Basic Maths Grand Test - Q7

If a person visits his dentist, suppose the probability that he will have his teeth cleaned is 0.48, the probability that he will have a cavity filled is 0.25, the probability that he will have a tooth extracted is 0.20, the probability that he will have a teeth cleaned and a cavity filled is 0.09, the probability that he will have his teeth cleaned anda tooth extracted is 0.12, the probability that he will have a cavity filled and a tooth extracted is 0.07, and the probability that he will have his teeth cleaned, a cavity filled,and a tooth extracted is 0.03. What is the probability that a person visiting his dentist will have at least one of these things done to him ?

reshown Nov 20

Please explain this ?

answered Nov 21 by (6,330 points)

Let

probability that he will have his teeth cleaned be $P(TC)$

probability that he will have a cavity filled be $P(CF)$

probability that he will have a tooth extracted be $P(TE)$

Given that

$P(TC)=0.48,P(CF)=0.25,P(TE)=0.20,P(TC\capCF)=0.09,P(CF\capTE)=0.07,P(TC\capTE)=0.12,P(TC\capCF\capTE)=0.03$

$P(TC\cupCF\cupTE)=P(TC)+P(CF)+P(TE)-P(TC\capCF)-P(CF\capTE)-P(TC\capTE)-P(TC\capCF\capTE)$

$P(TC\cupCF\cupTE)=0.48+0.25+0.20-0.09-0.07-0.12-0.03$

$P(TC\cupCF\cupTE)=0.93-0.31$

$P(TC\cupCF\cupTE)=0.62$

answered Nov 21 by (2,720 points)