Question

In Akutan, Alaska, men are 77% of the population. It is also known 11.3% of

Akutan males smoke cigars while 2.1% of Akutan females smoke cigars. One

member of the population is selected at random for a survey involving cell

phone carriers

Express the cigar smoking data as conditional probabilities.


Find the

probability that the selected subject does not smoke cigars given that the

subject is male

Answer 1

Kindly check explanation

Explanation:

Given the following :

Proportion of males, P(M) = 77% = 0.77

Proportion of females = ( 1 - proportion of males) = (1 - 0.77) = 0.23

Percentage of males who smoke cigar = 11.3% = 0.113

Percentage of female who smoke cigar = 2.1% = 0.021

Expressing cigar smoking Data as conditional probability :

P(male and smoking) = P(M n C) = 0.113

P(Female and smoking) = P(F n C) = 0.021

Probability of smoking cigar Given the person is a male :

P(C | M) = P(M n C) / P(M)

Probability of smoking cigar Given person is a female :

P(C | F) = P(F n C) / P(F)

Find the probability that the selected subject does not smoke cigars given that the subject is male?

No smoking Given Male = 1 - P(C | M)

P(C | M) = P(M n C) / P(M)

P(C | M) = 0.113 / 0.77

P(C | M) = 0.1467

1 - P(C | M)

1 - 0.1467

= 0.8533