困難的數(probability )，請解答

(a)find the patient has got both dental and eye diseases.

= patients with dental diseases + patients with eye diseases - patients with either dental or eye diseases

= (15+11-21)%

=5% (1/20)

b)The patient has got a dental disease, find the probability that he has got an eye disease as well.

=(the patient has got both dental and eye diseases)/(The patient has got a dental
disease)

=5%/15% by part a)

=1/3

c)The patient has got an eye disease, find the probability that he has got a dental disease as well.

=(the patient has got both dental and eye diseases)/(The patient has got a eye
disease)

=5%/11% by part a)

=5/11

let D- suffer from dental disease
C- suffer from eye disease
P(D)=0.15
P(E)=0.11
P(D U E)=0.21

P(D U C) = P(D) + P(E) - P(D n E) [Can be prove by venn diagram]
P(D n E) = P(D) + P(E) - P(D U E)
= 0.15+0.11-0.21
= 0.05 (1/20)

P(E | D) = P(D n E) / P(D) [By difinition]
= 0.05/0.15
= 0.33 (1/3)

P(D | E) = P(D n E) / P(E) [By difinition]
= 0.05/0.11
= 0.4545 (5/11)