Given data,

The number of balls each player has to play is 200.

The player who hits maximum number of six will win.

Step 1

a) The probability that Tendulkar hits the one six is,

The probability that he hits six at 3rd ball is,

\(\displaystyle{P}={\frac{{{1}}}{{{2}}}}\)

The probability that he hits six at 4th ball is,

\(\displaystyle{P}={\frac{{{2}}}{{{3}}}}\)

Similarly, the probability that he hits six at 200th ball is,

\(\displaystyle{P}={\frac{{{198}}}{{{199}}}}\).

The probability of one six in 200 ball is,

\(\displaystyle{P}={\frac{{{198}}}{{{199}}}}\times{\frac{{{197}}}{{{198}}}}\times\ldots\ldots\times{\frac{{{2}}}{{{3}}}}\times{\frac{{{1}}}{{{2}}}}\)

\(\displaystyle={\frac{{{1}}}{{{199}}}}\)

Step 2

b)The probability that Tendulkar hits 100 hits is,

Consider, P(k, n) be the probability of Tendulkar hitting k sixes in n balls. Here, \(\displaystyle{0}{<}{k}{<}{n}\)

The probability is calculated as,

\(\displaystyle{P}{\left({k},{n}\right)}={\frac{{{k}}}{{{n}-{1}}}}\)

Here,

\(\displaystyle{k}={100}\)

\(\displaystyle{n}={200}\)

Substituting the values then,

\(\displaystyle{P}{\left({100},{200}\right)}={\frac{{{100}}}{{{199}}}}\)