A BAG CONTAINS 3 RED CHIPS, 2 BLUE CHIPS AND 1 WHITE CHIP. IF 2 CHIPS ARE CHOSEN FROM THE BAG WITHOUT REPLACEMENT DETERMINE THE PROBABILITY THAT THEY ARE OF DIFFERENT COLORS
You can calculate the different combinations to get different colours, but you can also calculate the probability P of getting the same colours, and the required probability is 1-P.
get two reds: (3/6)*(2/5)=1/5
get two blues: (2/6)*(1/6)=1/18
Probability of getting two reds or two blues: (1/5)+(1/18)=23/90
Probability of not getting two of the same colour = 1-(23/90)=67/90
To determine the probability that two chips chosen from the bag without replacement are of different colors, we need to first calculate the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When two chips are chosen from the bag without replacement, the total number of possible outcomes can be calculated using the combination formula.
The formula for combination is: nCr = n! / (r!(n - r)!)
Where "n" is the total number of items and "r" is the number of items being chosen.
In this case, we have a total of 3 red chips, 2 blue chips, and 1 white chip in the bag. So, n = 6 (3 red + 2 blue + 1 white) and r = 2 (as we are choosing 2 chips).
Using the combination formula, the total number of possible outcomes is:
6C2 = 6! / (2!(6 - 2)!) = (6 * 5 * 4 * 3 * 2 * 1) / ((2 * 1) * (4 * 3 * 2 * 1)) = 15
Number of favorable outcomes:
To determine the number of favorable outcomes where two chips of different colors are chosen, we need to consider the different combinations of colors.
There are three possible cases:
1) One red chip and one blue chip.
2) One red chip and one white chip.
3) One blue chip and one white chip.
For each case, we multiply the number of chips available for that color and the number of chips available for the other color.
Case 1: 3 red chips * 2 blue chips = 6 favorable outcomes
Case 2: 3 red chips * 1 white chip = 3 favorable outcomes
Case 3: 2 blue chips * 1 white chip = 2 favorable outcomes
Total number of favorable outcomes = 6 + 3 + 2 = 11
Finally, we can calculate the probability of drawing two chips of different colors 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 = 11 / 15 ≈ 0.73
Therefore, the probability that two chips chosen from the bag without replacement are of different colors is approximately 0.73.