Explanation Definition: If X is a random variable for the number of successes in n independent and identical repetitions of an experiment with success and failure as two possible outcomes and if p is a probability of success, then the probability for k success is defined as, P ( X = k ) = ( n k ) p k ( 1 − p ) n − k Here, k = 0 , 1 , ⋅ ⋅ ⋅ , n . Calculation: Consider a person who claims to have extrasensory perception who states that she can read mental images 90 % of the time. It is agreed to grant her claim if she can correctly identify the mental image at least five out of six times. The probability of granting claim to the ESP person is required. This means that the probability of correctly identifying at least 5 times is required. This is a binomial distribution because there are fixed number of trials. The trails are independent and the probability is the same for all trials. Define X as the number of times the mental images are identified. In this part, she is only guessing. As there are only two possible outcomes of either can guess or cannot guess, the probability of making a correct guess is 0.50. So, p = 0.50 . Hence, n = 6 , X = 5 , p = 0.5 . Use the probability formula and substitute these values to calculate the required probability. P ( X ≥ 5 ) = P ( X = 5 ) + P ( X = 6 ) = ( 6 5 ) ( 0.5 ) 5 ( 1 − 0.5 ) 6 − 5 + ( 6 6 ) ( 0 To determine b) To find: The probability of denying claim to the ESP person if she claims that she really have the ability and says can read mental images 90 % of the time.

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 13.6, Problem 55PS

To determine

a)

To find:

The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90% of the time.

To determine

b)

To find:

The probability of denying claim to the ESP person if she claims that she really have the ability and says can read mental images 90% of the time.

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Chapter 13.6, Problem 54PS

Chapter 13.6, Problem 56PS

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Chapter 13 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 13.1 - IN YOUR OWN WORDS What is the difference between...Ch. 13.1 - IN YOUR OWN WORDS Define probabilities?Ch. 13.1 - Prob. 3PS Ch. 13.1 - Prob. 4PS Ch. 13.1 - Prob. 5PS Ch. 13.1 - Prob. 6PS Ch. 13.1 - Prob. 7PS Ch. 13.1 - Prob. 8PS Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...Ch. 13.1 - Give the probabilities in Problems 9-11 in decimal...

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a) To find: The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90 % of the time.

Solution Summary: The author calculates the probability of granting claim to the ESP person if she is only guessing.

Videos

a)

To find:

The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90% of the time.

b)

To find:

The probability of denying claim to the ESP person if she claims that she really have the ability and says can read mental images 90% of the time.

Want to see the full answer?

Chapter 13 Solutions

a) To find: The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90 % of the time.

Solution Summary: The author calculates the probability of granting claim to the ESP person if she is only guessing.

Videos

a) To find: The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90% of the time.

b) To find: The probability of denying claim to the ESP person if she claims that she really have the ability and says can read mental images 90% of the time.

Want to see the full answer?

Chapter 13 Solutions

a)

To find:

The probability of granting claim to the ESP person if she is only guessing and says can read mental images 90% of the time.

b)

To find:

The probability of denying claim to the ESP person if she claims that she really have the ability and says can read mental images 90% of the time.