A supposed coffee connoisseur claims she can distinguish between a cup of instant coffee and a cup of drip coffee 75% of the time. You give her 6 cups of coffee and tell her that you will grant her claim if she correctly identifies at least 5 of the 6 cups.
(a) What are her chances of having her claim granted if she is in fact only guessing
(b) What are her chances of having her claim rejected when in fact she really does have the ability she claims?
[Round your answer to 4 decimal places.]
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I would try as follows:
a) if she is just guessing, the the possibility of being right is 50%, and 50% for being wrong (since these are the only choices) in each trial. her claim will be granted in two cases: either she gets 5 right out of 6 or 6 out of 6, so
P(her claim granted)= P(being right 5 times)+P(being right 6 times)=0.5^5*0.5+0.5^0.5=1/32
b) in this case (she has the ability that she's claims), P(being right)=0.75 and P(being wrong)=0.25..
her claims will be rejected if she gets less than 5 right answers, either 4,2,3,1 or 0 right answers.. but this is the same as 1-P(her claim granted), hence
P(her claim rejected)=1-P(her claim granted)=1-P(5 right answers)-P(6 right answers)=