Question 13.8: Determine the number of runs and the values of n1 and n2 in ......

a. There are four runs, as shown.

\underbrace{\text { M M }}_{1} \quad \underbrace{\text { FFF }}_{2} \quad \underbrace{M}_{3} \quad \underbrace{\text { FF }}_{4}

There are 3 M’s and 5 F’s, so n_{1}=3 and n_{2}=5.

b. There are three runs, as shown.

\underbrace{\mathrm{H}}_{1} \quad \underbrace{\mathrm{T}}_{2} \quad \underbrace{\mathrm{HHH}}_{3}

There are 4 heads and 1 tail, so n_{1}=4 and n_{2}=1.

c. There are six runs, as shown.

\underbrace{\text { A }}_{1} \quad \underbrace{\text { B }}_{2} \quad \underbrace{\text { A A A }}_{3} \quad \underbrace{\text { B B }}_{4} \quad \underbrace{\text { A }}_{5} \quad \underbrace{\text { B B B }}_{6}

There are 5 A’s and 6 B’s, so n_{1}=5 and n_{2}=6.