A box contains 6 red balls, 4 white balls, and 5 green balls. If three balls are drawn in succession without being replaced, what is the probability that they are drawn in the order red, white, green?
Pr(R,W, then G)=6/15 * 4/14*5/13
check that.
4/91
12/5
To find the probability of drawing the balls in a specific order (red, white, green), we can use the concept of conditional probability.
Step 1: Determine the total number of possible outcomes.
The total number of balls in the box is 6 red + 4 white + 5 green = 15 balls. When three balls are selected without replacement, the total number of possible outcomes is given by the number of ways we can arrange 15 balls in groups of 3. This can be calculated using the formula for combinations, denoted as "C(n, r)", where n is the total number of items and r is the number of items chosen at a time. In this case, it is C(15, 3).
Step 2: Determine the number of favorable outcomes.
To draw the balls in the order red, white, green, we need to choose one red ball first (6 options), then one white ball from the remaining balls (4 options), and finally one green ball from the remaining balls (5 options). The number of favorable outcomes is the product of the number of options in each step since each step is dependent on the previous one.
Step 3: Calculate the probability.
The probability is the ratio of favorable outcomes to total outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Given that the number of favorable outcomes is (6 * 4 * 5) and the total number of outcomes is C(15, 3), we can substitute these values into the formula to calculate the probability.