Question

In a survey of 200 ladies, it was found that 142 like coffee, while 58 dislike it.
Find the probability that a lady chosen at random
(i) likes coffee
(ii) dislikes coffee

Answer 1

Total number of ladies = 200
Number of ladies who like coffee = 142

Number of ladies who dislike coffee = 58

Let E₁ and E₂ be the events that the selected lady likes and dislikes coffee, respectively.Then,
(i) P(selected lady likes coffee) = P(E₁) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{ladies}\mathrm{who}\mathrm{like}\mathrm{coffee}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{ladies}}=\frac{142}{200}=0.71$

(ii)​ P (selected lady dislikes coffee) = P(E₂) = ​$\frac{\mathrm{Number}\mathrm{of}\mathrm{ladies}\mathrm{who}\mathrm{dislike}\mathrm{coffee}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{ladies}}=\frac{58}{200}=0.29$


REMARK: In the given survey, the only possible outcomes are E₁ and E₂ and ​P(E₁) + ​P(E₂) = (0.71 + 0.29) = 1