A bag contains 7 red chips and 9 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that the two chips are the same color?
To get the first red chip = 7/16, for the second 6/15. The probability of both occurring is found by multiplying the individual probabilities.
To get the first blue chip = 9/16, for the second 8/15. The probability of both occurring is found by multiplying the individual probabilities.
The probability of getting either 2 blue or two red is found by adding the probabilities of your two previous answers.
pig
2/7
To find the probability that the two chips are the same color, we need to calculate the probabilities of two scenarios: both chips being red and both chips being blue.
Let's start by finding the probability of both chips being red. In the bag, there are a total of 7 red chips and 16 chips in total (7 red + 9 blue). When we select the first chip, the probability of choosing a red chip is 7/16, since there are 7 red chips out of 16 chips in total. After removing one chip from the bag, there are now 6 red chips left, and 15 chips in total. So, the probability of selecting another red chip is now 6/15.
To find the probability of both chips being red, we multiply the probabilities together: (7/16) * (6/15) = 42/240 = 7/40.
Similarly, if we calculate the probability of both chips being blue, the calculation would be: (9/16) * (8/15) = 72/240 = 3/10.
Finally, to find the probability of the two chips being the same color, we add the probabilities of both chips being red and both chips being blue: 7/40 + 3/10 = 35/160 + 48/160 = 83/160.
Therefore, the probability that the two chips selected are the same color is 83/160.