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 1

Answer:

Assuming that people cannot taste a difference between bottled water and tap water.

hence there will be a zero chance that even one of them is able to differentiate

Answer 2

Answer:

0.01953125

Step-by-step explanation:

Assuming that people cannot taste a difference between bottled water and tap water, then probability of correctly identifying tap water or bottled water is  equal ie p=0.5

let X be the number of participants who correctly identify tap water, then X forms a random variable with Binomial (9,0.5) distribution.

$f(x)=(\left {{n} \atop {x}} \right.)*  P^x * (1-P)^{n- x}\\\\f(x)=(\left {{9} \atop {x}} \right.)*  0.5^x * 0.5^{n- x}, x=0,1,2,..,9$

probability that at least 8 of the 9 participants will correctly identify the tap water is written as $p(X\geq 8)$

which is equivalent to  

$P(x\geq 8)=P(x=8)+P(x=9)\\\\P(x\geq 8)= 9C8*0.5^8*0.5^{(9-8)}+9C9*0.5^9*0.5^{(9-9)}\\\\P(x\geq 8)=0.01953125$