You have a box containing 13 purple balls, 17 orange 15 green and 11 white balls. What is the probability you pull 2 orange balls followed by a white ball?
Total of (13+17+15+11)=56 balls,
out of which 17 are orange and 11 are white.
Assume no replacement of balls.
The first orange: 17 out of 56 (17/56)
The second orange: 16 out of 55 (16/55)
The white: 11 out of 54 (11/54)
The probability of pulling in the given order is the product of the three fractions.
To find the probability of pulling 2 orange balls followed by a white ball, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of balls in the box: 13 purple + 17 orange + 15 green + 11 white = 56 balls.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes.
The number of favorable outcomes is the product of pulling 2 orange balls followed by 1 white ball.
The number of ways to choose 2 orange balls from 17 is calculated using the combination formula: C(17, 2) = 17! / (2! * (17-2)!), which simplifies to 136.
The number of ways to choose 1 white ball from 11 is simply 11.
Therefore, the number of favorable outcomes is 136 * 11 = 1496.
The total number of possible outcomes is the number of ways to choose 3 balls from 56 balls: C(56, 3) = 56! / (3! * (56-3)!), which simplifies to 27720.
So, the probability of pulling 2 orange balls followed by a white ball is 1496/27720 ≈ 0.054 or 5.4%.