# In a survey of 200 ladies, it was found that 142 like coffee, while 58 dislike it.

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

Solution:

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 $)=P\left(E_{1}\right)=\frac{\text { Number of ladies who like coffee }}{\text { Total number of ladies }}=\frac{142}{200}=0.71$

(ii) $P$ (selected lady dislikes coffee) $=P\left(E_{2}\right)=\frac{\text { Number of ladies who dislike coffee }}{\text { Total number of ladies }}=\frac{58}{200}=0.29$

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