A bag contains 3 red balls,5 blue balls and 7 green balls two are picked without replacement, what is the probability that both are different colour, they are of same colour
15 balls, so
P(R,R) = 3/15 * 2/14
P(B,B) = 5/15 * 4/14
P(G,G) = 7/15 * 6/14
P(2 same) = sum of the above
15 balls
first red = 3/15
second red = 2/14
both red = 3/15 * 2/14 = 1/5 * 1/7 = 1/35
first blue = 5/15 = 1/3
second blue 4/14 = 2/7
both blue = 2/21
first green = 7/15
second green = 6/14 = 3/7
both green = 7/15 * 3/7 = 1/5
now add 1/35 + 2/21 + 1/5 = about .0286 + .0952 + .2
idfk
Well, well, well. Looks like we have a colorful question here!
To calculate the probability that both balls are of different colors, we need to consider all the possible combinations.
First, let's find the total number of balls in the bag: 3 red + 5 blue + 7 green = 15 balls.
For the first ball, we have 15 choices. After picking that ball, we have 14 balls left.
Now, let's see how many different color combinations we can have:
Different color combinations: 3 (red and blue), 3 (red and green), and 5 (blue and green).
So, the total number of combinations for different color balls is 3 + 3 + 5 = 11.
To find the probability, we divide the number of favorable outcomes (11) by the total number of possibilities (15):
Probability of picking balls of different colors: 11/15 ≈ 0.73
Now, for the probability of picking balls of the same color, we simply subtract the probability of the opposite scenario from 1:
Probability of picking balls of the same color: 1 - 0.73 = 0.27
So, there's approximately a 0.73 chance that the two balls will be of different colors and a 0.27 chance that they will be of the same color.
Colorful probabilities, aren't they?
To find the probability, we need to determine the total number of outcomes and the number of favorable outcomes.
1. Probability that both balls are of different colors:
To find the probability of picking two balls of different colors, we need to consider all possible combinations.
First, let's calculate the total number of outcomes when picking two balls from the bag without replacement. Since there are a total of 15 balls in the bag, the first ball has 15 options. After picking the first ball, there are 14 balls remaining in the bag, so the second ball has 14 options. Therefore, the total number of outcomes is 15 * 14 = 210.
Next, let's calculate the number of favorable outcomes, which means picking two balls of different colors.
We can pick a red ball and then any of the remaining 12 balls. So, we have 3 red * 12 non-red = 36 favorable outcomes.
Similarly, we can pick a blue ball and then any of the remaining 13 balls, giving us 5 blue * 13 non-blue = 65 favorable outcomes.
Finally, we can pick a green ball and then any of the remaining 10 balls, resulting in 7 green * 10 non-green = 70 favorable outcomes.
The total number of favorable outcomes is 36 + 65 + 70 = 171.
Therefore, the probability of picking two balls of different colors is 171/210 ≈ 0.8143.
2. Probability that both balls are of the same color:
To find the probability of picking two balls of the same color, we'll consider each color separately.
For red balls, we have 3 red balls, so we can choose 2 red balls in C(3, 2) = 3 ways.
Similarly, for blue balls, we have 5 blue balls, giving us C(5, 2) = 10 ways.
For green balls, we have 7 green balls, and we can choose 2 green balls in C(7, 2) = 21 ways.
The total number of ways to choose two balls of the same color is 3 + 10 + 21 = 34.
Therefore, the probability of picking two balls of the same color is 34/210 ≈ 0.162.
So, to summarize:
- The probability that both balls are different colors is approximately 0.8143.
- The probability that both balls are of the same color is approximately 0.162.
Please note that the probabilities are approximate, rounded to four decimal places.