Heads or Tails

Probability Level 3

Ali and Qasim play a game. In this game, a fair coin is tossed for a sequence of 50 times. Each time a head comes up Ali wins 1 Rupee from Qasim and each time a tail comes up Ali loses 1 Rupee to Qasim.

For example, if they had tossed the coin 5 times and the course of the game was like HTTHT then in this game Ali would have lost 1 rupee to Qasim.

The probability that Ali will win 20 rupees from Qasim is approximately $A \times 10^{-B}$ , where $A$ and $B$ are positive integers with $A$ is a single-digit. Give $A + B$ as your answer.

The answer is 5.

1 solution

Ali Qureshi
Jul 10, 2016

For Ali to win 20 rupees there must be 35 heads and 15 tails. We fill find the probability of this event.

There are $2^{50}$ different possible games. And among these there are $50 C 35$ games in which there are 35 heads.

Therefore the probability of winning 20 Rupees is $50 C 35$ / $2^{50}$ = approx $2 \times 10^{-3}$

Heads or Tails

The answer is 5.

1 solution

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