Solve the problem.An experiment was conducted by having a group of children solve a puzzle. It was found that of those who had solved the puzzle on a given trial, 40% could solve it on the next trial. And of those who couldn't solve the puzzle on a given trial, 10% could solve it on the next trail. At the present time, 80% of the children solved the puzzle on the current trial, but 20% did not. Assume that this process can be modeled as a Markov process.(a) Write the transition matrix. Label the columns and rows, using S for "able to solve" and NS for "not able to solve."(b) What percent of the children will be able to solve the puzzle on the next trial?(c) After many trials, what proportion of the children will fail to solve the puzzle on each trial?
What will be an ideal response?
| (a) | S | NS |
 ? |  |
| (b) | 34% |
| (c) |  |
Mathematics
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