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 determine the total number of possible outcomes and the number of favorable outcomes.
Let's start by finding the total number of possible outcomes. In the first draw, you have 93 balls to choose from, and in the second draw, you have 92 balls to choose from, and so on. In total, there are 93 * 92 * 91 * ... * 78 possible outcomes for 16 draws. We can represent this mathematically as 93 P 16, which is the permutation formula for 93 objects taken 16 at a time.
The formula for the permutation of n objects taken r at a time is given by:
nPr = n! / (n - r)!
Now let's find the number of favorable outcomes, which is the number of ways to choose 13 yellow balls from 34 yellow balls. This is represented mathematically as 34C13, which is the combination formula for 34 objects taken 13 at a time.
The formula for the combination of n objects taken r at a time is given by:
nCr = n! / (r! * (n - r)!)
Therefore, the probability of withdrawing 13 balls of yellow color in 16 draws can be calculated as the number of favorable outcomes divided by the total number of possible outcomes:
Probability = (34C13 * (93 P 16)) / (93 P 16)
Calculating these values can be time-consuming and error-prone without the help of a calculator or a computer program. You can use statistical software or online calculators to get an accurate result.