We are given this table which is Benford law for these questions they are used for filling your taxes:

k= p(X=k)
1 0.301
2 0.176
3 0.125
4 0.097
5 0.079
6 0.067
7 0.058
8 0.051
9 0.046

1.) If you select two numbers randomly from any where on your taxes what is the probability of selecting a number that starts with 2 and a number that starts with 5 in any order

2.) If you randomly select a number on your taxed what is the probability that it will NOT begin with a number 4?

3.) If you select three numbers randomly from anywhere on your taxes what is the probability that all three numbers starts with the number 1 OR that none of the numbers start with the number 1?

Please show work I want to understand how to do these..

1) If I am looking at this correctly, I don't see any number that starts with 2, but I see one number that ends with 5 You probability is .079

2) I don't see any number beginning with 4. The probability that it won't be a 4 is the sum of all of the probabilities in your list which should = 1.

3) I don't see numbers starting with 1. I only see 2. So, the problem says that all 3 numbers start with 1. I would have to say 0.

You can add up all of the probabilities of the numbers that don't start with one.

Or you can add up the probabilities for the two numbers that do start with 1 and subtract it from 1.

Sure! I'll walk you through each question step by step.

1.) If you select two numbers randomly from anywhere on your taxes, you want to find the probability of selecting a number that starts with 2 and a number that starts with 5 in any order.

To solve this, we'll use the concept of independent events. Since the order doesn't matter, we can calculate the probability of each event separately and then multiply them together.

The probability of selecting a number that starts with 2 is given as 0.176, and the probability of selecting a number that starts with 5 is given as 0.079.

So, the probability of selecting a number that starts with 2 and another number that starts with 5 in any order is:
P(2 and 5) = P(2) * P(5)
= 0.176 * 0.079
= 0.013904
≈ 0.014

Therefore, the probability of selecting a number that starts with 2 and a number that starts with 5 in any order is approximately 0.014.

2.) If you randomly select a number on your taxes, you want to find the probability that it will NOT begin with the number 4.

To solve this, we'll use the complement rule. The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

Since the probabilities given in the table represent the likelihood of the numbers 1, 2, 3, etc. occurring as the first digit, we can subtract the probability of the number 4 occurring from 1.

The probability of selecting a number that starts with 4 is given as 0.097. So, the probability of NOT selecting a number that starts with 4 is:
P(not 4) = 1 - P(4)
= 1 - 0.097
= 0.903

Therefore, the probability of randomly selecting a number on your taxes that does NOT begin with the number 4 is 0.903.

3.) If you select three numbers randomly from anywhere on your taxes, you want to find the probability that all three numbers start with the number 1 OR that none of the numbers start with the number 1.

To solve this, we'll calculate the probabilities separately for each case and then add them together.

The probability of a number starting with 1 is given as 0.301. So, the probability of all three numbers starting with 1 is:
P(all 1s) = P(1) * P(1) * P(1)
= 0.301 * 0.301 * 0.301
≈ 0.027172201

Similarly, the probability of a number NOT starting with 1 is given by the sum of the probabilities of all other numbers (2-9):
P(not 1) = P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)
= 0.176 + 0.125 + 0.097 + 0.079 + 0.067 + 0.058 + 0.051 + 0.046
= 0.799

So, the probability of none of the three numbers starting with 1 is 0.799.

To find the probability of either all three numbers starting with 1 OR none of them starting with 1, we'll add the two probabilities together:
P(all 1s or none 1s) = P(all 1s) + P(not 1)
= 0.027172201 + 0.799
≈ 0.826172201

Therefore, the probability that all three numbers start with the number 1 OR none of them start with the number 1 is approximately 0.826.