Expected colour runs in a biased row of 25 cells

A row has $25$ cells. Each cell is coloured black with probability $\tfrac34$ and white with probability $\tfrac14$, independently. A component is a maximal block of neighbouring cells sharing one colour; for example BBWBWWWBBW has $6$ components. What is the expected number of components in the row?

$10$. The number of components is $1$ plus the number of neighbouring pairs whose colours differ. Two neighbours agree with probability $\tfrac9{16}+\tfrac1{16}=\tfrac58$, so they differ with probability $\tfrac38$, and there are $24$ pairs: $1+24\cdot\tfrac38=10$.