Discussion Forum

From the city population , the probabilty of  selecting a male or smoker is  $\frac{7}{10}$ , a male smoker is $\frac{2}{5}$ and a male, if a smoker is already selected , is $\frac{2}{3}$ . Then , the probability of 

Answer:

Explanation:

Suppose , A : a male is selected

 B: a smoker is selected 

 Given:

$P(A\cup B)=\frac{7}{10}, P(A\cap B)=\frac{2}{5}$ and    $P(\frac{A}{B})=\frac{2}{3}$

 The probability of selecting a smoker

$P(B)=\frac{P(A\cap B)}{P(\frac{A}{B})}$

=$\frac{2\times3}{5\times2}=\frac{3}{5}$

The  probability  of selecting  a non-smoker So, P(B)=1-P(B)

$=1-\frac{3}{5}=\frac{2}{5}$

 The probabilty of selecting a male 

$P(A)=P(A\cup B)+P(A\cap B)-P(B)$

$=\frac{7}{10}+\frac{2}{5}-\frac{3}{5}$

$=\frac{7+4-6}{10}=\frac{1}{2}$

 The probability of selecting  a smoker, if a male  is first  selected , is given by

$P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}$

=$\frac{2}{5}\times\frac{2}{1}=\frac{4}{5}$