There are 30 different colored pencils in a box. What is the probability that the orange pencil and then the green pencil will be chosen at random, without replacement? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answer
Answer
Final Answer: The probability that the orange pencil and then the green pencil will be chosen at random, without replacement, is approximately \(\boxed{0.0023}\).
Step 1 ：The problem is asking for the probability of choosing the orange pencil first and then the green pencil from a box of 30 different colored pencils, without replacement.
Step 2 ：The total number of outcomes is the total number of ways we can choose 2 pencils from 30, which is \(\binom{30}{2}\) or 435.
Step 3 ：The number of ways the event can occur is 1, as there is only one way to choose the orange pencil first and then the green pencil.
Step 4 ：The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. So the probability is \(\frac{1}{435}\).
Step 5 ：Using a calculator, we find that \(\frac{1}{435}\) is approximately 0.0022988505747126436.
Step 6 ：Final Answer: The probability that the orange pencil and then the green pencil will be chosen at random, without replacement, is approximately \(\boxed{0.0023}\).
