Among the contestants in a competition are 44 women and 26 men. if 5 winners are randomly selected, what is the probability that they are all men?
are you Mike?
http://www.jiskha.com/display.cgi?id=1279157840
prob = C(26,5)/C(70,5) = .005435
or
prob = 26/70*25/69*24/68*23/67*22/66 = .005435
Yes i am, i made a mistake on the first one, just wanted to make sure i had the right answer.
To find the probability that all 5 winners are men, we need to calculate the ratio of the number of favorable outcomes (all men) to the number of possible outcomes (total contestants).
1. First, let's determine the total number of contestants:
Total contestants = Number of women + Number of men
Total contestants = 44 women + 26 men
Total contestants = 70
2. Next, we need to calculate the number of ways to choose 5 winners from the total contestants. We can use the combination formula, denoted as C(n,r), which calculates the number of ways to choose r items from a set of n items without regard for the order:
In this case, we want to choose 5 winners from 70 contestants, so the number of ways is given by C(70,5). The formula for combination is:
C(n,r) = n! / (r! * (n-r)!)
Plugging in the values, we get:
C(70,5) = 70! / (5! * (70-5)!)
3. Now, let's calculate the number of ways to choose 5 winners from only the men. We can use the combination formula again, but this time with only the number of men as the total contestants:
In this case, we want to choose 5 winners from 26 men, so the number of ways is given by C(26,5). The formula for combination is:
C(n,r) = n! / (r! * (n-r)!)
Plugging in the values, we get:
C(26,5) = 26! / (5! * (26-5)!)
4. Finally, we can find the probability by dividing the number of ways to choose all men by the total number of ways to choose any 5 winners:
Probability = Number of ways to choose all men / Total number of ways to choose 5 winners
Probability = C(26,5) / C(70,5)
Performing the calculations, we get:
Probability = 65,780 / 12,103,014
Probability ≈ 0.00543
Therefore, the probability that all 5 winners are men is approximately 0.00543, or 0.543%.
To find the probability that all 5 winners are men, we need to determine the total number of possible outcomes and the total number of outcomes where all winners are men.
Total number of possible outcomes can be calculated using combinations. In this case, we need to select 5 winners from a pool of 70 contestants (44 women + 26 men). So, the total possible outcomes can be calculated as:
Total possible outcomes = C(70, 5)
Next, we need to determine the number of outcomes where all 5 winners are men. Since there are 26 men, we need to select 5 men from a pool of 26. So, the number of outcomes where all winners are men can be calculated as:
Number of outcomes where all winners are men = C(26, 5)
Finally, we can calculate the probability by dividing the number of outcomes where all winners are men by the total number of possible outcomes:
Probability = Number of outcomes where all winners are men / Total possible outcomes
Now, let me calculate it for you.