Connected Components I

You are given 15 squares arranged in a row. Each square is independently colored either black with probability $\frac{1}{3}$ or white with probability $\frac{2}{3}$ . A connected component is defined as a maximal sequence of adjacent squares that are all the same color. For example, in the coloring BBWWBBB, there are three connected components: the first two black squares form one component, the next two white squares form another, and the final three black squares form the third. What is the expected number of connected components in such a randomly colored row?

Enter your answer rounded to 5 decimal places.