I'm thinking of TWO numbers between 1 and 4 and so are you, what are the odds that we will have ATLEAST 1 number in common?
To determine the odds of having at least one number in common between the two sets of numbers, we first need to find the total number of possible outcomes.
In this case, each set of numbers can be any combination of two numbers between 1 and 4. Since there are 4 options for each number in a set, the total number of outcomes can be calculated by multiplying the number of options for each number (4) by itself: 4 * 4 = 16.
Next, we need to determine the number of outcomes where at least one number is common. To do this, we consider the following possibilities:
1. One number is common: There are 4 possible numbers that can be common (1, 2, 3, or 4). For each common number, there are 3 options for the other number (since it can be any of the remaining 3 numbers). Therefore, there are 4 * 3 = 12 outcomes where only one number is common.
2. Both numbers are common: There are 4 possible common numbers (1, 2, 3, or 4). For each common number, there is only 1 option for the other number, as it must be the same common number. Therefore, there are 4 * 1 = 4 outcomes where both numbers are common.
To find the total number of outcomes where at least one number is common, we add the outcomes from the two possibilities above: 12 + 4 = 16.
Finally, we calculate the odds by dividing the number of favorable outcomes (16) by the total number of possible outcomes (16). This results in a probability of 16/16, which simplifies to 1 or 100%.
Therefore, the odds that we will have at least one number in common between the two sets of numbers is certain or 100%.