Three balls are drawn together from a bag containing 4 white, 5 black, and 6 red balls. Find the probability that they include no white ball.
there are 11 non-white balls
so prob = 11/15 x 10/14 x 9/13
Oh, I see. Thank you! Probability is not my subject...
To find the probability that three balls drawn together from the bag contain no 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 possible outcomes:
The total number of balls in the bag is 4 white + 5 black + 6 red = 15 balls.
When three balls are drawn together, the total number of possible outcomes can be calculated using permutations.
Total possible outcomes = 15P3 = (15!)/(15-3)! = (15!)/(12!) = (15x14x13) / (3x2x1) = 455
Next, let's determine the number of favorable outcomes (no white balls):
Since we don't want any white balls among the three selected, we need to choose all three balls from the black and red ones only.
Number of favorable outcomes = 11P3 = (11!)/(11-3)! = (11!)/(8!) = (11x10x9)/(3x2x1) = 165
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total possible outcomes:
Probability = Number of favorable outcomes / Total possible outcomes
= 165 / 455
= 0.3626 (rounded to four decimal places)
Therefore, the probability that three balls drawn together from the bag include no white ball is approximately 0.3626.