MHB Gaming machine : The probability of winning

AI Thread Summary
The probability of winning at a gaming machine is 25%, and players can calculate various outcomes using binomial distribution. For 20 rounds, the probability of winning exactly five times can be computed with the formula P(5|20) = C(20,5) * 0.25^5 * 0.75^15. Similarly, probabilities for winning five times in ten rounds and winning ten times in ten rounds can be derived using the respective binomial formulas. The discussion confirms that the assumption of a fair and independent gaming machine validates these calculations. Understanding these probabilities helps players gauge their chances of winning over multiple rounds.
mathmari
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Hey! :o

At a gaming machine the probability of winning is 25%. A player plays 20 rounds.

  1. Which is the probability that he wins exactly five times?
  2. Which is the probability that in ten rounds he wins five times?
  3. Which is the probability that in ten rounds he wins ten times?
  4. Which is the probability that in twenty tries he wins zero times?

Do we use at each case the binomial distribution? (Wondering)

  1. $$P(5\mid 20)=\binom{20}{5}0.25^5\cdot 0.75^{15}$$
  2. $$P(5\mid 10)=\binom{10}{5}0.25^5\cdot 0.75^{5}$$
  3. $$P(10\mid 10)=\binom{10}{10}0.25^{10}\cdot 0.75^{0}$$
  4. $$P(0\mid 20)=\binom{20}{0}0.25^0\cdot 0.75^{20}$$
 
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We are making the assumption that the gaming machine is fair that is that the the goes are independent. If this is the case then your results are indeed correct. Well done
 
IanCg said:
We are making the assumption that the gaming machine is fair that is that the the goes are independent. If this is the case then your results are indeed correct. Well done

Thank you very much! (Smile)
 
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