Final answer:
To find the probability that the San Jose Sharks win at least three games in the upcoming month, we can use the concept of the binomial distribution. We calculate the probability of winning exactly k games using the binomial distribution formula and add up the probabilities for winning three games, four games, five games, and so on, up to twelve games. The answer is d) 0.4301.
Step-by-step explanation:
To find the probability that the San Jose Sharks win at least three games in the upcoming month, we can use the concept of the binomial distribution. The binomial distribution is used when there are only two possible outcomes in each trial, in this case, a win or a loss. The formula for the binomial distribution is:
P(X = k) = (nCk) * p^k * (1-p)^(n-k)
Where P(X = k) is the probability of getting exactly k successes in n trials, (nCk) is the number of combinations of n items taken k at a time, p is the probability of success in one trial, and (1-p) is the probability of failure in one trial.
- To find the probability that the San Jose Sharks win at least three games, we need to find the sum of the probabilities of winning three games, four games, five games, and so on, up to twelve games.
- Using the binomial distribution formula, we can calculate the probability of winning k games in a month. Since we know that the probability of winning any given game is 0.3694 (p = 0.3694) and there are 12 games in a month (n = 12), we can substitute these values into the formula for each value of k.
- Finally, we add up the probabilities for winning three games, four games, five games, and so on, up to twelve games, to find the probability that the San Jose Sharks win at least three games in the upcoming month.
The answer to this question is d) 0.4301.