Problemas
If the probability that the Islanders will beat the Rangers in a game is 0.62. what is the probability that the Islanders will win exactly one out of three games in a series against the Rangers?Round your answer to the nearest thousandth.
Roztwór
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veterano · Tutor durante 12 años
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(193 Votos)
Respuesta
To solve this problem, we can use the binomial probability formula. The binomial probability formula is used to find the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.The binomial probability formula is given by:P(X = k) = (n choose k) * p^k * (1-p)^(n-k)Where:- P(X = k) is the probability of obtaining k successes in n trials- n is the number of trials- k is the number of successes- p is the probability of success in a single trial- (1-p) is the probability of failure in a single trialIn this case, we want to find the probability that the Islanders will win exactly one out of three games in a series against the Rangers. So, we have:n = 3 (number of games in the series)k = 1 (number of games the Islanders will win)p = 0.62 (probability of the Islanders winning a single game)Plugging these values into the binomial probability formula, we get:P(X = 1) = (3 choose 1) * 0.62^1 * (1-0.62)^(3-1)P(X = 1) = 3 * 0.62 * 0.38^2P(X = 1) = 3 * 0.62 * 0.1444P(X = 1) = 0.2676Rounding this to the nearest thousandth, we get:P(X = 1) ≈ 0.268Therefore, the probability that the Islanders will win exactly one out of three games in a series against the Rangers is approximately 0.268.