In a test for ESP, the experimenter looks at cards that are hidden from the subject. Each card contains a star, a circle, a wavy line, or a square. An experimenter looks at each of 100 cards. The subject attempts to read the experimenter's mind and name the shape on each card. What is the probability that the subject gets more than 35 correct if the subject does not have ESP and is just guessing? please show calculations to help understand.

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In a test for ESP, the experimenter looks at cards that are hidden from the subject. Each card contains a star, a circle, a wavy line, or a square. An experimenter looks at each of 100 cards. The subject attempts to read the experimenter's mind and name the shape on each card. What is the probability that the subject gets more than 35 correct if the subject does not have ESP and is just guessing?

please show calculations to help understand. 

Expert Solution
Step 1: Determine the variable

In this case, each of the subjects has the only option of guessing a card "correctly" (defined as success) or "incorrectly" (defined as failure). For a considered number of n cards (i.e., the number of trials, n<) with a defined probability of correctly guessing a card (i.e., the suuccess probability, p is fixed), the random variable "X as the number of correctly guessed cards" is considered to follow Binomial distribution.



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