Problem

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

Solution

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 \(\boxed{0.0023}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8476/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download