A bag contains 3 black balls,four white balls and 5 red balls.Three balls are removed without replacement,what is the probability of obtaining one of each balls
To find the probability of obtaining one of each ball, we need to consider the following:
Step 1: Finding the total number of ways to choose 3 balls out of the 12 balls in the bag.
Step 2: Finding the number of ways to choose one black ball, one white ball, and one red ball.
Step 3: Calculating the probability by dividing the number of favorable outcomes by the total number of outcomes.
Let's break down each step:
Step 1: Finding the total number of ways to choose 3 balls out of the 12 balls in the bag.
To find the total number of ways, we can use the concept of combinations. The total number of ways to choose 3 balls out of 12 is denoted as C(12, 3) and can be calculated using the formula:
C(n, r) = n! / (r! * (n - r)!)
where "n" is the total number of items (balls in this case) and "r" is the number of items chosen without replacement.
In this case, we have:
n = 12 (total number of balls in the bag)
r = 3 (number of balls being chosen without replacement)
C(12, 3) = 12! / (3! * (12 - 3)!)
C(12, 3) = 12! / (3! * 9!)
Step 2: Finding the number of ways to choose one black ball, one white ball, and one red ball.
To find the number of ways to choose one black ball, one white ball, and one red ball, we need to consider the number of balls in each color.
For the black balls: We have 3 black balls, so we can choose 1 out of 3 in C(3, 1) ways.
For the white balls: We have 4 white balls, so we can choose 1 out of 4 in C(4, 1) ways.
For the red balls: We have 5 red balls, so we can choose 1 out of 5 in C(5, 1) ways.
To find the number of ways to choose one of each ball, we multiply these together:
Number of ways to choose one of each ball = C(3, 1) * C(4, 1) * C(5, 1)
Step 3: Calculating the probability.
Finally, we calculate the probability by dividing the number of favorable outcomes (choosing one of each ball) by the total number of outcomes (choosing any 3 balls from the bag).
Probability = Number of ways to choose one of each ball / Total number of ways to choose 3 balls
Probability = (C(3, 1) * C(4, 1) * C(5, 1)) / C(12, 3)
Simplifying further will give you the final probability.
I hope this explanation helps!
There are 12 balls in all, so
P(black,white,red) = 3/12 * 4/11 * 5/10
There are 6 permutations of those colors, so ...