in Construction Materials and Management recategorized by
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Contractor $\text{X}$ is developing his bidding strategy against Contractor $\text{Y}$. The ratio of $\text{Y’s}$ bid price to $\text{X’s}$ cost for the $30$ previous bids in which Contractor $\text{X}$ has competed against Contractor $\text{Y}$ is given in the table

$\begin{array}{|lc|c|}\hline
&\text{Ratio of $\text{Y’s}$ bid price of $\text{X’s}$ cost } & \text{Number of bids}\\ \hline &\text{$1.02$} & \text{$6$} \\ \hline &\text{$1.04$} & \text{$12$}\\ \hline
&\text{$1.06$} & \text{$3$} \\ \hline
&\text{$1.10$} & \text{$6$}  \\ \hline
&\text{$1.12$} & \text{$3$} \\ \hline 
 \end{array}$

Based on the bidding behaviour of the Contractor $\text{Y}$, the probability of winning against Contractor $\text{Y}$ at a mark up of $8\%$ for the next project is

  1. $0\%$
  2. more than $0\%$ but less than $50\%$
  3. more than $50\%$ but less than $100\%$
  4. $100\%$
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