There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fraction.
are you sure about the 144?
Misread the question, read it as 'of the same colour.'
So we need
1 - (25/144 + 16/144 + 9/144)
Well, let's clown around with some math here!
First, let's determine the total number of possible outcomes. Since we're drawing two chips with replacement, there are 12 chips to choose from each time, giving us a total of 12 x 12 = 144 possible outcomes.
Now let's calculate the probability of selecting two chips of different colors. There are 5 blue chips to choose from on the first draw, and since we're replacing the chip, there are still 5 blue chips available for the second draw as well. So, the probability of selecting two blue chips is (5/12) x (5/12) = 25/144.
Similarly, there are 4 red chips to choose from on the first draw, and 4 remaining red chips for the second draw, giving us a probability of (4/12) x (4/12) = 16/144.
Lastly, there are 3 yellow chips to choose from on the first draw, and 3 remaining yellow chips for the second draw, resulting in a probability of (3/12) x (3/12) = 9/144.
Now, to find the overall probability of selecting two chips of different colors, we add up the probabilities of each individual case: (25/144) + (16/144) + (9/144) = 50/144.
So, the probability of selecting two chips of different colors is 50/144, which can be further reduced to 25/72.
Hey, look at that! We did some math, and it wasn't even that funny. Well, at least we tried!
To find the probability that the two selected chips are of different colors, we can first calculate the probability of drawing a chip of one color and then drawing a chip of a different color.
There are a total of 5 + 4 + 3 = 12 chips in the bag.
The probability of drawing a blue chip on the first draw is 5/12, as there are 5 blue chips out of 12 chips total.
After placing the first chip back into the bag, there are still 12 chips in total. Now, the probability of drawing a chip of a different color (red or yellow) is 9/12, as there are 4 red chips and 3 yellow chips left out of the 12 chips.
To find the probability of both events happening, we multiply the probabilities:
(5/12) * (9/12) = 45/144 = 5/16
Therefore, the probability that the two selected chips are of different colors is 5/16.
3 cases:
BB ---> (5/12)(5/12) = 25/144
RR ---> (4/12)(4/12) = 16/144
YY ---> (3/12)(3/12) = 9/144
add them up