Question

The Psychic Friends Network (PFN) received telephone calls in 1999 from over 1.5 million people. A journal article attempted to shed some light onto the credibility of the PFN. One of the psychic friends' psychics agreed to take part in the following experiment. 5 cards are shown to the “psychic” then shuffled, and one is chosen at random. The psychic will then try to identify which card was drawn without seeing it. Assume that the experiment was repeated 17 times and that the results of any two experiments are independent of one another.

Step 1 of 4:

If we assume that the psychic is a fake (i.e., they are merely guessing at the cards and have no psychic powers), how many of the 17 cards do we expect the psychic to guess correctly?
(Round your answer to the nearest integer.)

Step 2 of 4:

If the psychic is a fake, what is the probability that 5 cards will be guessed correctly out of 17 independent trials?
(Round your answer to 4 decimals.)

Step 3 of 4:

If the psychic is a fake, what is the probability that 3 or fewer cards will be guessed correctly out of 17 independent trials?
(Round your answer to 4 decimals.)

Step 4 of 4:

If the psychic is a fake, what is the probability that more than 3 but less than 7 cards will be guessed correctly out of 17 independent trials?
(Round your answer to 4 decimals.)

Answer 1

Solution:- Given that n = 17, 5 cards given to chose one

Hence probability of selecting card = 1/5 = 0.2

step 1 of 4:

Number of cards guested by the psychic : n*p = 17*0.2 = 3.4 = 4

step 2 of 4:

P(X = 5) = 0.1361

step 3 of 4:

P(X <= 3) = 0.5489

step 4 of 4 :

P(3 < X < 7) = P(4)+P(5)+P(6) = 0.2093+0.1361+0.0680 = 0.4134