Question

Consider 270 independent observations. The probability of event A in a particular experiment is 0.0035 . Choose the appropriate formula to calculate the probability that event A does not occur at all in these observations. Select one: 1. Moivre-Laplace local formula 2. Bernoulli formula 3. Poisson formula 4. Moivre-Laplace integral formula

Answer 1

The appropriate formula to calculate the probability that event A does not occur in the 270 independent observations is the Bernoulli formula. To calculate the probability that event A does not occur at all, we use the formula: P(A does not occur) = (1 - p)^n, where p is the probability of event A occurring and n is the number of trials. Plugging in the given values, we get: P(A does not occur) = (1 - 0.0035)^270 = 0.8131 (rounded to four decimal places).

Step-by-step explanation:

The appropriate formula to calculate the probability that event A does not occur in the 270 independent observations is the Bernoulli formula.

The Bernoulli formula calculates the probability of a specific number of successes or failures in a fixed number of independent trials. In this case, we are interested in the probability of no successes (A not occurring) in 270 trials.

To calculate the probability that event A does not occur at all, we use the formula: P(A does not occur) = (1 - p)^n, where p is the probability of event A occurring and n is the number of trials. Plugging in the given values, we get: P(A does not occur) = (1 - 0.0035)^270 = 0.8131 (rounded to four decimal places).