Calculate the probability of withdrawing 13 balls of yellow color in 16 draws from a bag of 93 balls having 38 red, 34 yellow and 21 pink balls.
To calculate the probability of withdrawing 13 balls of yellow color in 16 draws from a bag of 93 balls, we need to use the concept of combinations and the probability formula.
Step 1: Determine the total number of ways to choose 16 balls from the bag of 93 balls. This can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of balls in the bag (93 in this case) and r is the number of balls drawn (16 in this case).
So, nCr = 93! / (16!(93-16)!) = 93! / (16!77!)
Step 2: Determine the number of ways to choose 13 yellow balls from the bag. Since there are 34 yellow balls in the bag, we can calculate it using the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of yellow balls in the bag (34 in this case) and r is the number of yellow balls drawn (13 in this case).
So, nCr = 34! / (13!(34-13)!) = 34! / (13!21!)
Step 3: Calculate the probability by dividing the number of ways to choose 13 yellow balls by the total number of ways to choose 16 balls:
Probability = (Number of ways to choose 13 yellow balls) / (Number of ways to choose 16 balls)
Probability = (34! / (13!(34-13)!)) / (93! / (16!(93-16)!))
Therefore, the probability of withdrawing 13 balls of yellow color in 16 draws from the given bag is the calculated value using the formula above.