Final answer:
To find the probability of getting exactly k red balls when picking 20 balls uniformly out of a bucket containing 30 red balls and 70 blue balls, you need to use the concept of combinations and probability. The formula for calculating the probability is: P(exactly k red balls) = (number of ways to choose k red balls out of 30) * (number of ways to choose 20 - k blue balls out of 70) / (total number of ways to choose 20 balls out of 100). You can substitute different values of k into the formula to find probabilities for different numbers of red balls.
Step-by-step explanation:
To find the probability of getting exactly k red balls when picking 20 balls uniformly out of a bucket containing 30 red balls and 70 blue balls, we need to use the concept of combinations and probability.
The formula for calculating the probability is:
P(exactly k red balls) = (number of ways to choose k red balls out of 30) * (number of ways to choose 20 - k blue balls out of 70) / (total number of ways to choose 20 balls out of 100)
The number of ways to choose k objects out of a total of n objects is given by the combination formula: C(n,k) = n! / (k!(n-k)!)
For example, if we want to find the probability of getting exactly 5 red balls, the calculation would be:
P(exactly 5 red balls) = C(30,5) * C(70,15) / C(100,20)
You can substitute different values of k into the formula to find probabilities for different numbers of red balls.