a candy dish contains 10 cinnamon drops 10 lemons and 10 peppermints. if two two pieces of candy are chosen at a random what is the probablity of getting a cinnamon drop first and then a peppermint?
10/30 * 10/29
tenmarks
To find the probability of getting a cinnamon drop first and then a peppermint, we need to calculate the ratio of the favorable outcomes to the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes:
The total number of candies in the dish is 10 cinnamon drops, 10 lemons, and 10 peppermints. So, the total number of candies is 10 + 10 + 10 = 30 candies.
Step 2: Calculate the number of favorable outcomes:
To get a cinnamon drop first and then a peppermint, we need to choose one cinnamon drop out of the 10 cinnamon drops first, and then one peppermint out of the remaining 10 peppermints. This can be done in a sequence, so we can multiply these two events' probabilities.
The probability of choosing a cinnamon drop first is 10/30 (10 cinnamon drops out of 30 candies).
The probability of choosing a peppermint afterwards is 10/29 (as there are now 29 candies left in the dish after the first choice).
Multiplying these probabilities together gives (10/30) * (10/29) = 100/870.
Step 3: Simplify the probability:
To simplify the probability, we divide both the numerator and denominator by their greatest common divisor, which is 10.
(100/870) รท 10/10 = 10/87.
Therefore, the probability of getting a cinnamon drop first and then a peppermint is 10/87.