Question

Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y's bid price to X's cost for the 30 previous bids in which Contractor X has competed against Contractor Y is given in the Table.\[\begin{array}{|c|c|} \hline \textbf{Ratio of Y's bid price to X's cost} & \textbf{Number of bids} \\ \hline \text{1.02} & \text{6} \\ \hline \text{1.04} & \text{12} \\ \hline \text{1.06} & \text{3} \\ \hline \text{1.10} & \text{6} \\ \hline \text{1.12} & \text{3} \\ \hline \end{array}\]Based on the bidding behaviour of Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is

• A. 0%
• B. more than 0% but less than 50%
• C. more than 50% but less than 100%
• D. 100%

Hint:

To calculate the probability of winning based on past bids, count the number of bids that meet the required criteria and divide by the total number of bids.

Answer 1

The Correct Option is B

We are given the ratio of Y's bid price to X's cost for 30 previous bids. We need to calculate the probability of Contractor X winning against Contractor Y at a mark-up of 8%. A mark-up of 8% means the ratio of Y's bid price to X's cost should be less than or equal to: \[ \frac{X's \, cost + 8%}{X's \, cost} = 1.08. \] Now, we look at the ratios of Y's bid price to X's cost that are less than or equal to 1.08:
- For ratios 1.02, 1.04, 1.06, and 1.08, we are interested in the number of bids where the ratio is less than or equal to 1.08.
- The corresponding counts are:
- 1.02: 6 bids
- 1.04: 12 bids
- 1.06: 3 bids
- 1.10: 0 bids (this ratio exceeds 1.08)
- 1.12: 0 bids (this ratio exceeds 1.08)
The total number of bids where the ratio is less than or equal to 1.08 is: \[ 6 + 12 + 3 = 21 \, \text{bids}. \] The probability of winning against Contractor Y is the number of successful bids divided by the total number of bids: \[ \text{Probability} = \frac{21}{30} = 0.7 \text{or} 70%. \] Since this probability is more than 0% but less than 50%, the correct answer is (B). Final Answer: more than 0% but less than 50%