Twelve people are given two identical speakers to listen for differences, if any. Suppose that these people answered by guessing only. Find the probability that three people claim to have heard a difference between the two speakers.

Question

lgbasallote · Answer

i suppose binomial distribution is applicable here...since there are only two possible results (difference or no difference)

lgbasallote · Answer

so

n = 12
x = 3

$$\huge \implies _{12}C_3 (\frac 14)^3 (\frac 34)^9$$
yes?

lgbasallote · Answer

which gives 0.2581

lgbasallote · Answer

so the probability is 25.81%

lgbasallote · Answer

thanks

anonymous · Answer

lol

anonymous · Answer

i understood 12C3 but why 1/4 & 3/4?

lgbasallote · Answer

because of the formula $$\huge _nC_x (p)^x (q)^{n-x}$$
where:
n = total number of subjects
x = number of people taken from that n
p = probability of success
q = probability of failure

lgbasallote · Answer

anyway...you get a medal for replying

anonymous · Answer

that's what i didn't get. isn't p 1/2 because you want the person to detect the difference & there are only 2 possibilities?....i'm sorry if i'm bothering you...

lgbasallote · Answer

3/12 = 1/4

lgbasallote · Answer

am i wrong?

anonymous · Answer

*smacks himself in the head* oooh i get it.

lgbasallote · Answer

hmm you may be on to something... i might be wrong

lgbasallote · Answer

what I did was wrong. thanks for making me realize (now you really deserve that medal)

anonymous · Answer

i have to agree with whatever you say because i've never seen that formula & I have no idea what "probability of success" really means....

lgbasallote · Answer

i do though....and it seems i really am wrong