There are 3 red chips and 2 green chips. You win the game if you take out all the chips of the same color. What is the probability you take all the green chips out?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
3/5 * (3-1)/(5-1) * (3-2)/(5-2) = ?
To calculate the probability of taking out all the green chips, we need to determine the total number of possible outcomes and the number of favorable outcomes.
In this case, the total number of possible outcomes is the total number of ways to arrange all the chips. We have 5 chips in total, so the total number of possible outcomes is 5!.
Next, let's consider the number of favorable outcomes, which is the number of ways to arrange only the green chips. Since there are 2 green chips, the number of ways to arrange them is 2!.
Therefore, the probability of taking out all the green chips can be calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 2! / 5!
Now, let's compute the factorial terms:
2! = 2 x 1 = 2
5! = 5 x 4 x 3 x 2 x 1 = 120
Plugging these values into the equation:
Probability = 2 / 120 = 1 / 60
So, the probability of taking out all the green chips is 1/60.