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?
If there is no difference in ability to taste either water, the probability of correctly identifying tap water should be 50% or \(\frac{1}{2}\).
The probability that at least 8 of the 9 participants correctly identifying tap water can be found with the formula (given in the formula sheet):
$$ \binom{n}{x}p^x(1-p)^{n-x} $$
We need to find the probability of 8 correct and the probability of 9 correct and then add them together.
8 Participants Correct
$$ \binom{9}{8}\left(\frac{1}{2}\right)^8\left(1-\frac{1}{2}\right)^{9-8} $$
$$ \approx 0.01758 $$
9 Participants Correct
$$ \binom{9}{9}\left(\frac{1}{2}\right)^9\left(1-\frac{1}{2}\right)^{9-9} $$
$$ \approx 0.00195 $$
$$ 0.01758 + 0.00195 = \boxed{0.0195} $$