The table below describes the smoking habits of a group of asthma sufferers. Non

Question

The table below describes the smoking habits of a group of asthma sufferers.

Nonsmoker Light smoker Heavy smoker Total Male 347 50 39 436 Female 354 34 46 434 Total 701 84 85 870

(a) Find out the joint probability of Gender (rows) and Smoker (Columns)

(b) Find out the probability distribution for Gender

(c) Find out the probaility distribution for Smoker.

(d) What is probability that the selected person is a heavy given that this person is a woman?

i. Determine the probability directly from above counts.

ii. Determine the probability using multiplication rule.

Nonsmoker Light Smoker Heavy Smoker Total Male 347 50 39 436 Female 354 34 46 434 Total 701 84 85 870

Explanation / Answer

a) joint probability of gender and smoker

total n=870

joint probability of (male+non smoker) =P(M NS)= 347/870=0.3988=0.40

joint probability of (male+light smoker) =P(M LS)=50/870=0.0574=0.057

joint probability of (male+heavy smoker)=P(M HS)=39/870= 0.0448=0.045

joint probability of (female+non smoker) = P(F NS)=354/870=0.4068=0.41

joint probability of (female+light smoker) =P(F LS)=34/870=0.0390=0.039

joint probability of (female+heavy smoker)=P(F HS)=46/870= 0.0528=0.053

b) Find out the probability distribution for Gender

P(M)= P(M NS)+P(M LS)+P(M HS)

=0.40+0.057+0.045

P(M)=0.502

P(F)=  P(F NS)+P(F LS)+P(F HS)

=0.41+0.039+0.053

P(F)=0.502

c) Find out the probaility distribution for Smoker

P(NS)=P(M NS)+P(F NS)

=0.40+0.41

P(NS)=0.81

P(LS)=P(M LS)+P(F LS)

=0.057+0.039

P(LS)=0.096

P(HS)=P(M HS)+P(F HS)

=0.045+0.053

P(HS)=0.098

d) probability that the selected person is a heavy given that this person is a woman

=heavy smoker women/total women

=46/434

=0.10599

=0.106

The  probability that the selected person is a heavy given that this person is a woman is 0.106

Non smoker(NS) Light Smoker(LS) Heavy smoker(HS) Total Male(M) 347 50 39 436 Female(F) 354 34 46 434 Total 701 84 85 870

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.