A store sells bags of candies with three different flavors: cherry, lemon, and orange. Each bag contains 10 candies, with 4 cherries, 3 lemons, and 3 oranges. If you randomly pick 2 candies from the bag without replacement, what is the probability that both candies will be of the same flavor?
To calculate the probability of picking two candies of the same flavor without replacement, we need to consider the probabilities for each flavor separately and then add them together.

First, let's determine the probability of picking two cherry candies:

P(Cherry on first pick) = Number of cherries / Total number of candies
                                        = 4 / 10
                                        = 0.4

P(Cherry on second pick | Cherry on first pick) = Remaining cherries / Remaining candies
                                                                    = 3 / 9
                                                                    ≈ 0.3333

P(Two cherry candies) = P(Cherry on first pick) * P(Cherry on second pick | Cherry on first pick)
                                  = 0.4 * 0.3333
                                  ≈ 0.1333

Next, let's determine the probability of picking two lemon candies:

P(Lemon on first pick) = Number of lemons / Total number of candies
                                       = 3 / 10
                                       = 0.3

P(Lemon on second pick | Lemon on first pick) = Remaining lemons / Remaining candies
                                                                   = 2 / 9
                                                                   ≈ 0.2222

P(Two lemon candies) = P(Lemon on first pick) * P(Lemon on second pick | Lemon on first pick)
                                 = 0.3 * 0.2222
                                 ≈ 0.0667

Finally, let's determine the probability of picking two orange candies:

P(Orange on first pick) = Number of oranges / Total number of candies
                                         = 3 / 10
                                         = 0.3

P(Orange on second pick | Orange on first pick) = Remaining oranges / Remaining candies
                                                                     = 2 / 9
                                                                     ≈ 0.2222

P(Two orange candies) = P(Orange on first pick) * P(Orange on second pick | Orange on first pick)
                                   = 0.3 * 0.2222
                                   ≈ 0.0667

Now, we can add these probabilities together to find the overall probability of picking two candies of the same flavor:

P(Two candies of the same flavor) = P(Two cherry candies) + P(Two lemon candies) + P(Two orange candies)
                                                  ≈ 0.1333 + 0.0667 + 0.0667
                                                  ≈ 0.2667

So, the probability of picking two candies of the same flavor without replacement is approximately 0.2667 or 26.67%.