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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 contains the tap water. Assuming that people cannot taste a difference between bottled water, what is the probability that at least 8 of the 9 people will correctly identify the tap water?

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Answer:

The answer is [tex]\frac{1}{256}[/tex]

Step-by-step explanation:

If we assume that people cannot taste a difference between bottled water, then the probability of identifying tap water is 0.5

Thus, P(identify tap water)=0.5

The probability that at least 8 of the 9 people identify the tap water correctly is the sum of the probabilities

  • 8 of 9 people identified correctly or
  • 9 of 9 people identified correctly

Since P(identify tap water)=0.5 each probabilities are the same and equal to

[tex]0.5^9[/tex] =[tex]\frac{1}{512}[/tex]

So we have [tex]2*\frac{1}{512}[/tex] = [tex]\frac{1}{256}[/tex]

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