Questions - Basic Probability

Probability
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Ex15.1, 8 The distance (in km) of 40 engineers from their residence to their place of work were found as follows. What is the empirical probability that an engineer lives: less than 7 km from her place of work? Total number of engineers = 40 Number of engineers living less than 7 km from their place of work = 9 P(engineer lives less than 7 km from her place of work) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐  ๐๐๐ฃ๐๐๐ ๐๐๐ ๐  ๐กโ๐๐ 7๐๐ ๐๐๐๐ โ๐๐ ๐๐๐๐๐ ๐๐ ๐ค๐๐๐)/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐ ) = 9/40 Ex15.1, 8 (Method 1) The distance (in km) of 40 engineers from their residence to their place of work were found as follows. What is the empirical probability that an engineer lives: (ii) more than or equal to 7 km from her place of work? Total number of engineers = 40 Number of engineers living more than or equal to 7 km from their place of work = 40 โ 9 = 31 P(engineer lives less than 7 km from her place of work) = (๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐  ๐๐๐ฃ๐๐๐ ๐๐๐ ๐  ๐กโ๐๐ 7๐๐ ๐๐๐๐ โ๐๐ ๐๐๐๐๐ ๐๐ ๐ค๐๐๐)/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐ ) = 31/40 Ex15.1, 8 (Method 2) The distance (in km) of 40 engineers from their residence to their place of work were found as follows. What is the empirical probability that an engineer lives: (ii) more than or equal to 7 km from her place of work? P(engineer lives more than or equal to 7 km from her place of work) = 1 โ P(engineer lives less than 7 km from her place of work) = 1 โ 9/40 = (40 โ 9)/40 = 31/40 Ex15.1, 8 The distance (in km) of 40 engineers from their residence to their place of work were found as follows. What is the empirical probability that an engineer lives: (iii) within 1/2 km from her place of work? Total number of engineers = 40 Number of engineers living within 1/2 km from their place of work = 0 P(engineer living within 1/2 km from their place of work) =(๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐  ๐๐๐ฃ๐๐๐ ๐ค๐๐กโ๐๐ 1/2 ๐๐ ๐๐๐๐ ๐กโ๐๐๐ ๐๐๐๐๐ ๐๐ ๐ค๐๐๐)/(๐๐๐ก๐๐ ๐๐ข๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐ ) = 0/40 = 0