Chapter 4.4, Problem 24PSC

a)

To determine

To calculate: probability as per specified condition.

Answer to Problem 24PSC

  $\frac{1}{5}$

Explanation of Solution

Formula used: $\text{Probability}=\frac{\text{numbers of favourable outcomes}}{\text{total numbers of outcomes}}$

Calculation:

Total numbers of ways = C (6, 2) =15.

Favourable case is unordered pairs as follows: $\{(C,M),(M,E),(C,E)\}$

  $\therefore \text{Probability}=\frac{3}{15}=\frac{1}{5}$

b)

To determine

To calculate: Probability of three chosen points to be collinear.

Answer to Problem 24PSC

  $\frac{1}{10}$

Explanation of Solution

Formula used: $\text{Probability}=\frac{\text{numbers of favourable outcomes}}{\text{total numbers of outcomes}}$

Calculation:

Total numbers of ways = C (6, 3) =20.

Favourable case is only if A, M and B are chosen.

  $\therefore \text{Probability}=\frac{2}{20}=\frac{1}{10}$