To determine the probability of getting a number less than 2 or a prime number upon rolling a six-sided die, let's go through this step-by-step.
### Step 1: Understand the Problem
A six-sided die has the numbers 1, 2, 3, 4, 5, and 6. We need to find the probability of rolling a number that is either:
- Less than 2, or
- A prime number.
### Step 2: Identify Favorable Outcomes
#### Numbers Less than 2
- There is only one number on the die that is less than 2: 1.
#### Prime Numbers
To determine the prime numbers on a six-sided die, we list the numbers first: 1, 2, 3, 4, 5, 6. Then we identify which of these numbers are prime:
- 2 (prime)
- 3 (prime)
- 5 (prime)
So, the prime numbers are: 2, 3, and 5.
### Step 3: Combine the Favorable Outcomes
We combine the numbers less than 2 and the prime numbers, making sure we count each favorable outcome only once. Here are the favorable outcomes:
- Less than 2: 1
- Prime numbers: 2, 3, 5
Listed together, the unique favorable outcomes are: 1, 2, 3, 5.
### Step 4: Calculate the Number of Favorable Outcomes
There are 4 favorable outcomes in total: 1, 2, 3, and 5.
### Step 5: Determine the Total Number of Possible Outcomes
A six-sided die has 6 possible outcomes (1, 2, 3, 4, 5, 6).
### Step 6: Calculate the Probability
The probability [tex]\( P \)[/tex] of an event is given by:
[tex]\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \][/tex]
Substituting in our numbers:
[tex]\[ P(\text{less than 2 or prime number}) = \frac{4}{6} = \frac{2}{3} \][/tex]
### Step 7: Simplified Result
The final probability, simplified, is [tex]\( \frac{2}{3} \)[/tex] or approximately 0.67.
### Conclusion
Thus, the probability of rolling a number that is less than 2 or a prime number on a six-sided die is [tex]\( \frac{2}{3} \)[/tex], which is approximately 0.67.
