A coffee connoisseur claims that he can distinguish between a cup of instant coffee and a cup of percolator coffee 75% of the time. It is agreed that his claim will be accepted if he correctly identifies at least 5 of the 6 cups. Find his chances of having the claim i) accepted, ii) rejected, when he does have the ability he claims.

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coffentw · Accepted Answer

Step 1 Let p denote the probability of correct distinction between a cup of instant coffee and a cup of percolator coffee is made. Thus, we have, p=75%=75100=0.75 ∵q=1−p=1−0.75=0.25 If X denotes the number of correct distinctions done then by binomial probability, the probability of x correct distinctions out of n is given by, P(X=x)=nCxpxqn−x x=0,1,2,3..6 Step 2 The chance of the claim being accepted is given by, P(X≥5)=P(X=5)+P(X=6) =6C5(0.75)5(0.25)6−5+6C6(0.75)6(0.25)6−6 =0.355957+0.177979 =0.533936 Thus, the chance of the claim being accepted is 0.533936 Step 3 The chance of the claim being rejected is given by, P(X&amp;lt;5)=1−P(X≥5) =1−0.533936 =0.466064 Thus, the chance of the claim being rejected is 0.466064.

A coffee connoisseur claims that he can distinguish between a cup of instant cof

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