Question

Suppose that a friend of yours (named Muriel) from Britain claims to be able to tell by tasting whether if the milk was added before the brewed tea when preparing a cup of tea.

To check this claim, you've prepared 10 cups of tea of which some have milk added first and others have milk added last. For each tea, Muriel will guess whether the milk was added first or last.

Now, we are going to assume that your friend does NOT actually have the skill to tell whether milk was added first or last (meaning that her guess is random). Let X=number of correct guesses from 10 cups of tea tasting.

Find the probability that she guesses at least 6 correctly.

• 0.1776

• 0.3770

• 0.8332

• 0.2051

Answer 1

here, it is a binomial probability distribution,

because number of trails is fixed,n=10

only two outcome,either he is correct or wrong

trials are independent of each other.

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

since, he guess in random , there is only two options, either he is correct or wrong .so, probability of success = 1/2 =0.5

p=0.5

n=10

we need to find ,

P(X≥6) = 1-P(X<6) = 1 - ΣC(n,x)*p^x*(1-p)^(n-x) where x goes from 0 to 5

P(X≥6)=1-0.6230 = 0.3770

probability that she guesses at least 6 correctly is 0.3770