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 yellow balls in 16 draws, we can use the concept of combinations and the probability formula.
First, let's find the total number of ways to draw 16 balls from a bag of 93 balls. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where:
n is the total number of balls in the bag (93 in this case)
r is the number of balls to be drawn (16 in this case)
! denotes the factorial of a number
Plugging in the values:
C(93, 16) = 93! / (16! * (93-16)!)
Next, let's find the number of ways to draw 13 yellow balls from the bag. We can apply the combination formula again:
C(34, 13) = 34! / (13! * (34-13)!)
Now, we divide the number of favorable outcomes (drawing 13 yellow balls) by the total number of possible outcomes (drawing 16 balls):
P = C(34, 13) / C(93, 16)
Calculating this value will give us the probability of withdrawing 13 yellow balls in 16 draws from the given bag.