Need help with this. In a test for ESP (extrasensory perception), the experiment

Question

Need help with this. In a test for ESP (extrasensory perception), the experimenter looks a. cards.ha. arc hidden from the subject. Each card contains either a star, a circle, a wave, or a square. As the experimenter looks at each car s m turn, the subject names the shape on the card. If a subject simply guesses the shape on each card, what is the probability of a successful guess on a sing e car. Because the cards arc independent, the count of successes in 20 cards has a binomial distribution. What is the probability that a subject correctly guesses at least 10 of the 20 shapes? In many repetitions of this experiment with a subject who is guessing, how many cards will the subject guess correctly on the average? What is the standard deviation of the number of correct guesses?

Explanation / Answer

a) Probability is 1/4=0.25 [ each card contains either circle, star, wave and sqaure)

b) P(X>=10)=1-P(X<10)=1-0.986=0.014

P(X=0)=20C0(0.25)^0(0.25)^20=0.003, compute remaining probabilities till P(X=9) and add them.

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