A random sample of 415 children from England and the United States who completed a survey in a recent year was selected. Each student’s country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the two-way table.

Suppose we randomly select one of these students. Define events E: England, T: telepathy, and S: superstrength.

a. Find P(T | E). Interpret this value in context.

b. Given that the student did not choose superstrength, what’s the probability that this child is from England? Write your answer as a probability statement using correct symbols for the events.

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Country Superpower England U.S. Total Fly 54 45 99 Freeze time 52 44 96 Invisibility 30 37 67 Superstrength 20 23 43 Telepathy 44 66 110 Total 200 215 415