# Tendulkar is playing a cricket tournament in which each player can pla

Tendulkar is playing a cricket tournament in which each player can play 200 balls and the player who hits maximum sixes wins. Tendulkar hits a six on the first ball, but misses out on the second.
After that, the probability that he hits a six is equal the proportion of sixes that he has hit so far. For example, at the third ball, the probability is $$\displaystyle{\frac{{{1}}}{{{2}}}}$$.
(a) What is the probability that Tendulkar hits only one six?
(b) What is the probability that Tendulkar hits 100 sixes?

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Sevensis1977

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