An individual claims to have ESP (extra sensory perception). To determine the ex

Question

An individual claims to have ESP (extra sensory perception). To determine the extent of his ability, the numbers 1 to 5 are placed on one side of five cards (one number to a card). A card is then chosen at random and the individual is asked to identify the number on the selected card without looking. If the individual is merely guessing (that is picking a number at random), what is the probability that he will be correct? Suppose this procedure is repeated 30 times. If the individual is guessing each time, find the probability he gets 11 or more correct out of 30. If in fact this person gets 11 or more correct, would this suggest some extrasensory ability on his part or not? Explain. The launching of a space shuttle is sometimes cancelled (due to the weather, technical problems etc.). Suppose that past experience suggests about 20% of the scheduled launches have been cancelled. Consider the next 15 scheduled launches. Find the probability that at least 4 will be cancelled, fewer than 3 will be cancelled, more than 7 will NOT be cancelled. Find the mean (expected) number of cancellations. Find the variance and standard deviation.

Explanation / Answer

Solution:-

a) The probability that he will be correct is 0.20.

The probability that he will be correct =1/5=0.20

b) The probability that he will get eleven or more correct out of 30 is = 0.0256.

Probability of getting one correct answer in one try=p =0.2

Total number of trys = 30

x > or =11

By applying binomial distribution:-

P(x,n,p)= nCx* px *(1-p)(n-x)

P (x > 11) = 0.0256

c) No, the person doesn;t have extra sensory ability because the probability of getting 11 or more correct is 0.0256.

Although the chances are very less of getting 11 or more correct.

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