Question

Assuming that people cannot taste a 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

Answer 1

Complete question :

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 contains the tap water. Assuming that people cannot taste a 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?

Answer:

0.0196

Step-by-step explanation:

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

Here,

p = 0.5 ; q = 1 - p = 0.5

Number of trials, n = 9

P(x ≥ 9) = p(x = 8) + p(x = 9)

P(x = 8) = 9C8 * 0.5^8 * 0.5^1 = 0.0176

P(x = 9) = 9C9 * 0.5^9 * 0.5^0 = 0.0020

P(x =8) +. P(x =9) = 0.0176 + 0.0020 = 0.0196