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There are 50 workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects 2 workers (without replacement). What is the probability that NEITHER of the workers selected are left-handed? Round your answer to two decimal places.

There are 5050 workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects 22 workers (without replacement).\newlineWhat is the probability that NEITHER of the workers selected are left-handed?\newlineRound your answer to two decimal places.

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Q. There are 5050 workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects 22 workers (without replacement).\newlineWhat is the probability that NEITHER of the workers selected are left-handed?\newlineRound your answer to two decimal places.
  1. Total workers calculation: Determine the total number of workers and the number of left-handed workers.\newlineTotal workers = 5050\newlineLeft-handed workers = 66\newlineRight-handed workers = Total workers - Left-handed workers = 50−6=4450 - 6 = 44
  2. Probability of first worker not being left-handed: Calculate the probability that the first worker selected is not left-handed.\newlineThe probability that the first worker selected is not left-handed =Number of right-handed workersTotal number of workers=4450= \frac{\text{Number of right-handed workers}}{\text{Total number of workers}} = \frac{44}{50}
  3. Probability of second worker not being left-handed: Calculate the probability that the second worker selected is not left-handed after the first right-handed worker has been selected.\newlineSince one right-handed worker has been selected, there are now 4343 right-handed workers left and the total number of workers is reduced to 4949.\newlineThe probability that the second worker selected is not left-handed =Number of remaining right-handed workersRemaining total number of workers=4349= \frac{\text{Number of remaining right-handed workers}}{\text{Remaining total number of workers}} = \frac{43}{49}
  4. Probability of neither worker being left-handed: Multiply the probabilities from Step 22 and Step 33 to find the probability that neither of the two workers selected are left-handed.\newlineProbability that neither worker is left-handed = Probability first worker is not left-handed ×\times Probability second worker is not left-handed = 4450\frac{44}{50} ×\times 4349\frac{43}{49}
  5. Final probability calculation: Perform the calculation from Step 44 and round the answer to two decimal places.\newlineProbability that neither worker is left-handed = (4450)×(4349)≈0.7745(\frac{44}{50}) \times (\frac{43}{49}) \approx 0.7745\newlineRounded to two decimal places, the probability is approximately 0.770.77.

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