Question

your flight has been delayed: at denver international airport, 86% of recent flights have arrived on time. a sample of 12 flights is studied. (a) find the probability that all 12 of the flights were on time. the probability that all 12 of the flights were on time is. round the probabilities to at least four decimal places. part: 0 / 4 part 1 of 4

Explanation:

Step1: Identify the probability of a single - flight being on - time

The probability that a single flight is on time is $p = 0.86$.

Step2: Use the multiplication rule for independent events

Since the flights are assumed to be independent, the probability that all $n = 12$ flights are on time is given by the formula $P(X=12)=p^{n}$. Substitute $p = 0.86$ and $n = 12$ into the formula: $P(X = 12)=(0.86)^{12}$.

Step3: Calculate the result

$(0.86)^{12}\approx0.1422$.

Answer:

$0.1422$