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A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contain tap water. Assuming that people cannot taste the difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?
A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contain tap water. Assuming that people cannot taste the difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?
Final answer:The probability that at least 8 of the 9 participants will correctly identify the tap water is approximately 0.0195.Explanation:To calculate the probability that at least 8 of the 9 participants will correctly identify the tap water, we can use the binomial probability formula:P(X≥k) = 1 - P(X) { Where P(X≥k) is the probability of getting k or more successes.The probability of correctly identifying the tap water is 1/2 since there are two options (tap water or bottled water) and assuming they cannot taste the difference.The probability of getting 8 or more successes can be calculated by summing the probabilities of getting exactly 8, 9 successes:P(X≥8) = P(X=8) + P(X=9)= C(9, 8) * (1/2)^8 * (1/2)^1 + C(9, 9) * (1/2)^9 * (1/2)^0= 9 * (1/2)^8 * (1/2) + 1 * (1/2)^9= 9/512 + 1/512= 10/512= 5/256≈ 0.0195...