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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 $50$ 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). $\newline$ What is the probability that NEITHER of the workers selected are left-handed? $\newline$ Round your answer to two decimal places.

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Find probabilities using combinations and permutations

Full solution

Q. 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).

\newline

What is the probability that NEITHER of the workers selected are left-handed?

\newline

Round your answer to two decimal places.

Total workers calculation: Determine the total number of workers and the number of left-handed workers. $\newline$ Total workers = $50$ $\newline$ Left-handed workers = $6$ $\newline$ Right-handed workers = Total workers - Left-handed workers = $50 - 6 = 44$
Probability of first worker not being left-handed: Calculate the probability that the first worker selected is not left-handed. $\newline$ The probability that the first worker selected is not left-handed $= \frac{\text{Number of right-handed workers}}{\text{Total number of workers}} = \frac{44}{50}$
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. $\newline$ Since one right-handed worker has been selected, there are now $43$ right-handed workers left and the total number of workers is reduced to $49$ . $\newline$ The probability that the second worker selected is not left-handed $= \frac{\text{Number of remaining right-handed workers}}{\text{Remaining total number of workers}} = \frac{43}{49}$
Probability of neither worker being left-handed: Multiply the probabilities from Step $2$ and Step $3$ to find the probability that neither of the two workers selected are left-handed. $\newline$ Probability that neither worker is left-handed = Probability first worker is not left-handed $\times$ Probability second worker is not left-handed = $\frac{44}{50}$ $\times$ $\frac{43}{49}$
Final probability calculation: Perform the calculation from Step $4$ and round the answer to two decimal places. $\newline$ Probability that neither worker is left-handed = $(\frac{44}{50}) \times (\frac{43}{49}) \approx 0.7745$ $\newline$ Rounded to two decimal places, the probability is approximately $0.77$ .

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