# FINDING PROBABILITY USING A LIST

## About "Finding probability using a list"

Finding probability using a list :

We all know, how to calculate theoretical probability using tables and tree diagrams.

In this section, we are going to see, how theoretical probability can be calculated using lists.

The formula given below can be used to find the theoretical probability.

## Finding probability using a list - Example

The combination for Khiem’s locker is a 3-digit code that uses the numbers 1, 2, and 3. Any of these numbers may be repeated. Find the probability that Khiem’s randomly-assigned number is 222.

Solution :

Step 1 :

List all the codes that start with 1 and have 1 as a second digit.

(1, 1, 1)

(1, 1, 2)

(1, 1, 3)

Step 2 :

List all the codes that start with 1 and have 2 as a second digit.

(1, 2, 1)

(1, 2, 2)

(1, 2, 3)

Step 3 :

List all the codes that start with 1 and have 3 as a second digit.

(1, 3, 1)

(1, 3, 2)

(1, 3, 3)

Step 4 :

 Codes start with 2(2, 1, 1)(2, 1, 2)(2, 1, 3)(2, 2, 1)(2, 2, 2)(2, 2, 3)(2, 3, 1)(2, 3, 2)(2, 3, 3) Codes start with 3(3, 1, 1)(3, 1, 2)(3, 1, 3)(3, 2, 1)(3, 2, 2)(3, 2, 3)(3, 3, 1)(3, 3, 2)(3, 3, 3)

Step 5 :

Find the number of outcomes in the sample space by counting all the possible codes.

There are 27 such codes.

Step 6 :

Find the probability that Khiem’s locker code is 222.

Number of outcomes for  Khiem’s locker code 222  =  1

Probability (Code 222)  =  1/27

## Probability using a list - Practice question

Martha types a 4-digit code into a keypad to unlock her car doors. The code uses the numbers 1 and 0. If the digits are selected at random, what is the probability of getting a code with exactly two 0s ?

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