Chapter 1, Problem 19RP

Solution

a.

The probability that the selected point is the mid-point.

The probability that the selected point is the mid-point is $\frac{2}{5}$

Given: One of the five labelled point is selected.

Concept used: Here, we are using formula of probability which is

  $\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

Calculation: Here, the formula is $\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

Favorable outcomes = 2 and Total outcomes = 5

By putting the values in the given formula, we get

→ $\frac{2}{5}$

Conclusion: Hence, the probability that the selected point is the mid-point is $\frac{2}{5}$

b.

Probability that both the selected points are mid-points.

Probability that both the selected points are mid-points is $\frac{1}{10}$

Given: Two of the five points are randomly chosen.

Concept used: Here, we are using formula of probability which is

  $\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

Calculation: Here, the formula is $\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

Favorable outcomes = 1 and total outcomes = 10 putting these values in the given formula

→ $\frac{1}{10}$

Conclusion: Hence, Probability that both the selected points are mid-points is $\frac{1}{10}$