Question

Question Help Suppose that the probability that a randomly selected person who has recently married for the first time will be divorced within 2 years is 0.25​, and that the probability that a randomly selected person who has recently married for the second time will be divorced within 2 years is 0.5. Take a random sample of 25 people married for the first time and 25 people married for the second time. The sample is chosen such that no one in the sample is married to anyone else in the sample. Why is the binomial model inappropriate for finding the probability that exactly 4 of the 50 people in the sample will be divorced within 2 ​years? List all of the binomial conditions that are not met.

Answer 1

The trial are not dependent

Explanation:

The following four conditions must be met before Binomial probability experiment can be define, they are:

[1]. Each trial is independent, [2]. the trial must have two outcomes that is failure or success, [3]. fixed number of trials and [4]. success probability for each trial is the same.

Thus, the number of ways to choose the positions for success is given in equation (1) below as:

P(x) = n Cₓpˣ [1 - p]ⁿ⁻ˣ. ----------------------------------------------------------------------(1).

Where n-x = failure and 1 - p = probability and x = success.

For this question, three of the conditions mentioned above are met except for condition number one. This is so because the events are dependent. Therefore, the binomial condition that is not met is Each trial is independent.

NB: Why the events are dependent is because if the each husband divorce his wife, then the wife is also divorced.