Subjects probability

Football Match Probabilities

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Football Match Probabilities


1. Let's define the probabilities for a single football match: win = $p_w$, lose = $p_l$, draw = $p_d$. 2. Since these are the only outcomes, they must satisfy $p_w + p_l + p_d = 1$. 3. For 20 matches, each match is independent, so the combined probabilities for all matches are the product of individual match probabilities. 4. The probability that the team wins all 20 matches is $p_w^{20}$. 5. Similarly, the probability that the team loses all 20 matches is $p_l^{20}$. 6. The probability that all 20 matches end in draws is $p_d^{20}$. 7. If you want the probability of any combination of wins, losses, and draws over 20 matches, you would use the multinomial distribution, but for all matches having the same outcome, the above powers apply. 8. To summarize: - Probability all wins: $p_w^{20}$ - Probability all losses: $p_l^{20}$ - Probability all draws: $p_d^{20}$ This gives the probabilities of each match outcome happening in all 20 matches consecutively.