A bag contains 2 green balls and 1 red ball Two balls are randomly selected without replacement. What is the probability of selecting one of each colour
answer is
2/3
Ah, a game of "Color Roulette"! To calculate the probability of selecting one green ball and one red ball, we'll need to use our colors and counting skills.
In this scenario, we have a total of 3 balls: 2 green ones and 1 red one. When we draw the first ball, there are 3 options. Let's say we draw a green one. Now, only 2 balls are left, one of which is red. Therefore, the probability of drawing a green ball and then a red ball is (2/3) * (1/2) = 1/3.
So, the probability of selecting one green ball and one red ball is 1/3. Just remember, in this game, it's not about winning or losing, it's about making the game more colorful!
To find the probability of selecting one green ball and one red ball, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
We can select one green ball and one red ball in two ways:
- Selecting a green ball first, followed by a red ball.
- Selecting a red ball first, followed by a green ball.
Step 2: Determine the total number of possible outcomes.
To find the total number of possible outcomes, we need to calculate the total number of ways two balls can be selected without replacement from the bag. This can be found using the formula for calculating combinations.
Total number of possible outcomes = Combination(3 balls, 2 selected) = 3! / (2! * (3-2)!) = 3
Step 3: Calculate the probability.
The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 3
So, the probability of selecting one ball of each color is 2/3.
To determine the probability of selecting one green ball and one red ball, we need to calculate the probability of two different events: (1) selecting a green ball first and then a red ball second, and (2) selecting a red ball first and then a green ball second.
Let's break down the calculation step by step:
Step 1: Calculate the probability of selecting a green ball first and then a red ball second.
- There are 3 balls in total (2 green and 1 red) in the bag.
- The probability of selecting a green ball first is 2/3 because there are 2 green balls out of 3 total balls.
- After one ball is removed from the bag, only 2 balls remain (1 green and 1 red).
- The probability of selecting a red ball second is 1/2 because there is 1 red ball out of 2 remaining balls.
- The probability of both events happening in sequence is found by multiplying these probabilities: (2/3) * (1/2) = 1/3.
Step 2: Calculate the probability of selecting a red ball first and then a green ball second.
- Using the same logic as before, the probability of selecting a red ball first is 1/3 because there is 1 red ball out of 3 total balls.
- After removing one ball, now there are 2 balls remaining (2 green).
- The probability of selecting a green ball second is 2/2 or simply 1 because there are only green balls left.
- The probability of both events happening in sequence is again found by multiplying these probabilities: (1/3) * 1 = 1/3.
Step 3: Add the probabilities from both steps together to get the overall probability of selecting one of each color:
(1/3) + (1/3) = 2/3.
Therefore, the probability of selecting one green ball and one red ball when two balls are randomly chosen without replacement is 2/3.