Question

As men and women age, their risk of death increases. There are also health issues that can greatly impair older citizens' abilities to participate in activities and travel. Assume you are planning a 60 th high school reunion and are wondering how many of the older adults would be able to attend. If you know that 25 women and 21 men are still alive, and are told that exactly 10 of them will attend, what is the probability that you would have exactly five men and exactly five women attend? The probability that five men and five women attend is (Round to four decimal places as needed.)

Answer 1

To calculate the probability of having exactly five men and five women attend the reunion, we use the combination formula to find the number of possible combinations and then calculate the probability.

Step-by-step explanation:

To calculate the probability, we need to consider the total number of possible combinations for selecting 10 people out of the remaining 46 people (25 women and 21 men).

The number of ways to select 5 women from 25 is represented by the combination formula C(25, 5).

The number of ways to select 5 men from 21 is represented by the combination formula C(21, 5).

We can calculate the probability using the formula (C(25, 5) * C(21, 5)) / C(46, 10).

Plugging in the values, the probability that exactly 5 men and 5 women attend the reunion is approximately 0.0120 (rounded to four decimal places).

Answer 2

To find the probability of exactly five men and exactly five women attending the reunion, we can use the hypergeometric distribution. The solution is a probability of 0.1445.

Step-by-step explanation:

To find the probability that exactly five men and exactly five women attend the reunion, we can use the hypergeometric distribution. The hypergeometric distribution is used when sampling without replacement from a finite population where outcomes can be classified into two categories. In this case, the population consists of the men and women who are still alive.

To calculate the probability, we need to determine the number of ways to select 5 men and 5 women from the available men and women who are still alive. The total number of men who can attend is 21, and the total number of women who can attend is 25. Using the hypergeometric formula:

P(X = 5) = (C(21, 5) * C(25, 5)) / C(46, 10)

where C(n, r) represents the combination of n items taken r at a time, we can calculate the probability. The solution is:

P(X = 5) = 0.1445