Final answer:
To calculate the probability of winning 10 or more prizes from 12 tickets with 50-50 odds, we use the binomial probability formula and sum the probabilities for 10, 11, and 12 successes out of 12 trials.
Step-by-step explanation:
The question relates to the calculation of the probability of a specific outcome when buying a set of gaming table tickets in the context of a charity dinner. Specifically, it asks for the probability of winning 10 or more prizes given that each of the 12 tickets has a 50-50 chance of winning. This can be approached using binomial probability distribution, which can be calculated using the formula for binomial probability:
P(X = x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
- C(n, x) is the combination of n items taken x at a time.
- p is the probability of success on a single trial.
- n is the number of trials.
- x is the number of successes that result in a win.
To find the probability of winning 10, 11, or 12 prizes (out of 12), we would add up the individual probabilities:
P(X ≥ 10) = P(10) + P(11) + P(12)
Each P(x) would need to be calculated with the binomial formula using x as 10, 11, and 12 respectively and n as 12 because there are a total of 12 tickets. The resulting sum of these probabilities would give us the chance of winning 10 or more prizes.