consider the experiment of rolling a single
die.
What is the probability of rolling a number that is divisible
by 2 or 3?
4/6 probabilty
To find the probability of rolling a number that is divisible by 2 or 3 when rolling a single die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes:
Since we are rolling a single die, there are 6 different numbers that can appear on the die face: 1, 2, 3, 4, 5, and 6. Therefore, the total number of possible outcomes is 6.
Step 2: Determine the number of favorable outcomes:
We need to identify the numbers that are divisible by 2 or 3. Divisible by 2: The numbers 2, 4, and 6 are divisible by 2. Divisible by 3: The numbers 3 and 6 are divisible by 3.
To avoid counting duplicates (since 6 is divisible by both 2 and 3), we add the total number of individual outcomes for each condition and then subtract the intersection (6) once.
So the number of favorable outcomes is 3 (numbers divisible by 2) + 2 (numbers divisible by 3) - 1 (intersection) = 4.
Step 3: Calculate the probability:
Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
Therefore, the probability of rolling a number that is divisible by 2 or 3 is 4 (favorable outcomes) divided by 6 (total possible outcomes), which simplifies to 2/3 or approximately 0.6667.