Answer:
Explanation:
Since there are 4 equally sized teams and Kara is only assigned to one of them, the probability of Kara being assigned to the red team is:
Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes
Number of ways Kara can be on red team = 20/4 = 5 (since each team has 5 students)
Total number of possible outcomes = Total number of ways of dividing 20 students into 4 teams
To find the total number of ways of dividing 20 students into 4 teams, we can use the formula for combinations:
Total number of possible outcomes = C(20,5) x C(15,5) x C(10,5) x C(5,5)
where C(n,r) represents the number of ways to choose r items from a set of n items.
Simplifying the expression:
Total number of possible outcomes = (20! / (5!15!)) x (15! / (5!10!)) x (10! / (5!5!)) x (5! / (5!0!))
Total number of possible outcomes = 15,504,000
Therefore, the probability of Kara being on the red team is:
Probability of Kara being on red team = Number of ways Kara can be on red team / Total number of possible outcomes
Probability of Kara being on red team = 5 / 15,504,000
Probability of Kara being on red team = 0.0000323 (rounded to 7 decimal places)
So the probability of Kara being assigned to the red team is approximately 0.0000323 or 0.00323%.