Answer:
The probability is [tex]P(Z) = 0.0064 [/tex]
Step-by-step explanation:
From the question we are told that
The number of members is n = 15
Generally the number of ways of selecting two member from the fifteen members is mathematically represented as
[tex]K = ^{n}C_2 * 2![/tex]
Here C stands for combination hence we will be making use of the combination functionality in our calculator
[tex]K = ^{15}C_2 * 2 * 1 [/tex]
=> [tex]K = 78 * 2 * 1 [/tex]
=> [tex]K = 156 [/tex]
Gnerally the number of outcome that matches the outcome required by the committee(Which is reselecting the member who where the chairman and vice chairman of the board ) is m = 1
Generally the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and assigning them to their current positions is mathematically represented as
[tex]P(Z) = \frac{m}{K}[/tex]
=> [tex]P(Z) = \frac{1}{156}[/tex]
=> [tex]P(Z) = \frac{1}{156}[/tex]
=> [tex]P(Z) = 0.0064 [/tex]
