PLEASE HELP LAST PROBLEM DUE IN 30 MINUTES

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?

Question

PLEASE HELP LAST PROBLEM DUE IN 30 MINUTES

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?

anonymous · Answer

Her claim will be granted if she correctly identifies 5 cups or correctly identifies 6 cups.  We want to calculate the probabilities of guessing 5 by using the multiplication rule.  If she is guessing, then she will be correct 50% of the time or .5

P(5 correct answers) = .5 x .5 x .5 x .5 x .5 = .03125
P(6 correct answers) = .03125 x .5 = .015625

P(5 or 6) = .03125 + .015625 = .046875 = 4.6875%