A group of researchers are studying whether monozygotic twins possess extra sensory perception (ESP) They commenced by designing the following experiment The researchers chose the value of an integer d They selected a set of twins and asked each of the twins to think of an integer between 1 and d, and to write that number down on a sheet of paper The researchers then compared the numbers from the twins to see if they were the same (a)Suppose there is no ESP at all between the twins What is the probability that the twins would choose the same number (b)Again assuming no ESP, how large does d have to be so that the probability that the twins choose the same number is 1 in 1000 (i e , 0 001) or less (c)The researchers then recruited 500 sets of twins, and performed the same experiment on each set, using the value of d from part (b) Of the 500 sets oftwins, one set of twins wrote down the same number This set of twins were then announced in a media release that they had demonstrated ESP Is the claim of ESP justified

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A group of researchers are studying whether monozygotic twins possess extra-sensory perception (ESP). They commenced by designing the following experiment: The researchers chose the value

A group of researchers are studying whether monozygotic twins possess extra-sensory perception (ESP). They commenced by designing the following experiment:

The researchers chose the value of an integer d. They selected a set of twins and asked each of the twins to think of an integer between 1 and d, and to write that number down on a sheet of paper. The researchers then compared the numbers from the twins to see if they were the same.

(a)Suppose there is no ESP at all between the twins. What is the probability that the twins would choose the same number?
(b)Again assuming no ESP, how large does d have to be so that the probability that the twins choose the same number is 1 in 1000 (i.e., 0.001) or less?
(c)The researchers then recruited 500 sets of twins, and performed the same experiment on each set, using the value of d from part (b). Of the 500 sets oftwins, one set of twins wrote down the same number. This set of twins were then announced in a media release that they had demonstrated ESP. Is the claim of ESP justified?