Answer to Question #270431 in Statistics and Probability for Light

Question

table below shows the distribution of smokers and non – smokers by gender.

  Smokers Non – smokers Men 88 42 women 8 70

If one person is chosen at random find the probability that the person is:

A woman who smokes?

A non – smoker given that she is a woman

A man or a smoker.

(2 marks) 

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & Smokers & Non – smokers & Total \\ \hline Men & 88 & 42 & 130 \\ \hdashline Women & 8 & 70 & 78\\ \hdashline Total & 96 & 112 & 208\\ \end{array}$$

1.

$$P(W \& \ Smoker)=\dfrac{8}{208}=\dfrac{1}{26}$$

2.

$$P(Non-smoker|W)=\dfrac{70}{78}=\dfrac{35}{39}$$

3.

$$P(M\ or\ Smoker)=\dfrac{130+96-88}{208}=\dfrac{69}{104}$$