Lottery tickets are held by 56 men and 84 women. An equal percentage of men and women are older than 55. If there are 8 men over 55, what is the probability that the lottery winner will be either man of any age or a women over 55 years old.
To find the probability that the lottery winner will be either a man of any age or a woman over 55 years old, we need to first find the total number of people who meet this criteria and then divide it by the total number of people who hold lottery tickets.
First, let's find the total number of people who meet the criteria. We are given that there are 8 men over 55 years old. Since an equal percentage of men and women are older than 55, we can assume that there are also 8 women over 55 years old. So, the total number of people who meet the criteria is 8 (men) + 8 (women) = 16.
Next, let's find the total number of people who hold lottery tickets. It is given that there are 56 men and 84 women, so the total number of people with tickets is 56 (men) + 84 (women) = 140.
Now, we can calculate the probability. The probability is given by the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, the favorable outcomes are the 16 people who meet the criteria (8 men and 8 women over 55 years old), and the total number of possible outcomes is the total number of people with lottery tickets, which is 140.
Therefore, the probability is:
Probability = 16 (favorable outcomes) / 140 (total possible outcomes)
Probability = 0.114
So, the probability that the lottery winner will be either a man of any age or a woman over 55 years old is approximately 0.114, or 11.4%.