Jane is hiking in one of two areas; in both she may come across a rattlesnake. For the first area, the probability of seeing a rattle snake is 0.1, and for the second, it is 0.07. If Jane saw a rattle snake last time, she switches the areas; and if she did not see a snake, she keeps hiking in the same area.

(a) Write the transition matrix.

(b) Given that Jane last time hiked in the first area, find the probability that during 4 hikes each time she will switch the areas.