M L Aggarwal Solutions for Chapter: Probability, Exercise 1: Exercise 15

The distance (in $km$) of $40$ engineers from their residence to their place of work is found as follows:

$$\begin{gathered} 5 3 10 20 25 11 13 7 12 31 \\ 19 10 12 17 18 11 32 17 16 2 \\ 7 9 7 8 3 5 12 15 18 3 \\ 12 14 2 9 6 15 15 7 6 12 \end{gathered}$$

What is the empirical probability that an engineer lives less than $7 km$ from his/her place of work?

The distance (in $km$) of $40$ engineers from their residence to their place of work is found as follows:

$$\begin{gathered} 5 3 10 20 25 11 13 7 12 31 \\ 19 10 12 17 18 11 32 17 16 2 \\ 7 9 7 8 3 5 12 15 18 3 \\ 12 14 2 9 6 15 15 7 6 12 \end{gathered}$$

The distance (in $km$) of $40$ engineers from their residence to their place of work is found as follows:

$$\begin{gathered} 5 3 10 20 25 11 13 7 12 31 \\ 19 10 12 17 18 11 32 17 16 2 \\ 7 9 7 8 3 5 12 15 18 3 \\ 12 14 2 9 6 15 15 7 6 12 \end{gathered}$$

A company selected $4000$ households at random and surveyed them to find out a relationship between income level and the number of television sets in a home, The information so obtained is listed in the following table:

A company selected $4000$ households at random and surveyed them to find out a relationship between income level and the number of television sets in a home, The information so obtained is listed in the following table:

A company selected $4000$ households at random and surveyed them to find out a relationship between income level and the number of television sets in a home, The information so obtained is listed in the following table:

Two sections of class $IX$ of a school having $27$ students in each section appeared for mathematics olympiad. The marks obtained by them are given below:

$$\begin{gathered} 46, 31, 74, 68, 42, 54, 14, 61, 48, 37, 26, 8, 64, 57, 93, 72, 53, 59, 38, 16, 88, 56, \\ 46, 66, 45, 61, 54, 27, 27, 44, 63, 58, 43, 81, 64, 36, 49, 50, 76, 38, 47, 77, 62, \\ 53, 40, 71, 60, 45, 42, 34, 46, 40, 59, 42 \end{gathered}$$

One student is selected at random. Find the probability that selected student is having marks more than $49$.

Two sections of class $IX$ of a school having $27$ students in each section appeared for mathematics olympiad. The marks obtained by them are given below:

$$\begin{gathered} 46, 31, 74, 68, 42, 54, 14, 61, 48, 37, 26, 8, 64, 57, 93, 72, 53, 59, 38, 16, 88, 56, \\ 46, 66, 45, 61, 54, 27, 27, 44, 63, 58, 43, 81, 64, 36, 49, 50, 76, 38, 47, 77, 62, \\ 53, 40, 71, 60, 45, 42, 34, 46, 40, 59, 42 \end{gathered}$$

One student is selected at random. Find the probability that selected student is having marks between $39$ and $100$.