6. A certain test for telepathic communication consists of 10 questions. On each

Question

6. A certain test for telepathic communication consists of 10 questions. On each question, a subject is shown a card with one of 5 symbols on it. That subject attempts to communicate the image on the card to her partner, who then selects one of the symbols as the correct one. The score, X, is a count of the number of correct answers. If the partner is just randomly guessing, the probability distribution of X is given by the table below: 1 4 10 P(X) .10.26 .30.20.09.0301.001 0001.00001 .000001 (Probabilities do not quite add to 1 due to rounding) Now use the distribution to find the probability of the following events: a. b. c. d. e. Event A: the partner gets at least 5 correct Event B: the partner gets an odd number of answers correct Event C: the partner gets fewer than 7 correct EventAn B EventAUB g. Event AUC h. Event An Bn C

Explanation / Answer

a) P(A) = P(atleast 5 correct) = P(5) + P(6) + P(7) + P(8) + P(9) + P(10)

P(A) = P(atleast 5 correct) = 0.03 + 0.01 + 0.001 + 0.0001 + 0.00001+ 0.000001

P(A) = P(atleast 5 correct) = 0.041111

b) P(B) = P(odd number of correct) = P(1) + P(3) + P(5) + P(7) + P(9)

P(B) = P(odd number of correct) = 0.26 + 0.2 + 0.03 + 0.001 + 0.00001

P(B) = P(odd number of correct) =0.49101

c) P(C) = P(less than 7 correct) = 1 - P(7) - P(8) - P(9) - P(10)

P(C) = P(less than 7 correct) = 1 - 0.001 - 0.0001 - 0.00001- 0.000001

P(C) = P(less than 7 correct) = 0.998889

d) P(A and B) = P(5) + P(7) + P(9)

P(A and B) = 0.03 + 0.001 + 0.00001 = 0.03101

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