![]() The series ends when the winning team wins 4 games. In the world series, there are two baseball teams. If you can follow the logic of this solution, you have a good understanding of the material covered in the tutorial, to this point. Solution: This is a very tricky application of the binomial distribution. What is the probability that the world series will last 4 games? 5 games? 6 games? 7 games? Assume that the teams are evenly matched. This would be the sum of all these individual binomial probabilities.ī(x = 0 100, 0.5) + b(x = 1 100, 0.5) +. Therefore, the binomial probability is:ī(2 5, 0.167) = 5C 2 * (0.167) 2 * (0.833) 3ī(2 5, 0.167) = 0.161 Cumulative Binomial ProbabilityĪ cumulative binomial probability refers to the probability that the binomial random variable falls within a specified range (e.g., is greater than or equal to a stated lower limit and less than or equal to a stated upper limit).įor example, we might be interested in the cumulative binomial probability of obtaining 45 or fewer heads in 100 tosses of a coin (see Example 1 below). Solution: This is a binomial experiment in which the number of trials is equal to 5, the number of successes is equal to 2, and the probability of success on a single trial is 1/6 or about 0.167. What is the probability of getting exactly 2 fours? If the probability of success on an individual trial is P, then the binomial probability is:ī( x n, P) = * P x * (1 - P) n - x Given x, n, and P, we can compute the binomial probability based on the binomial formula:īinomial Formula. Suppose a binomial experiment consists of n trials and results in x successes. For example, in the above table, we see that the binomial probability of getting exactly one head in two coin flips is 0.50. The binomial probability refers to the probability that a binomial experiment results in exactly xsuccesses.
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