A six-sided die with sides numbered 1 through 6 is tossed twice. What is the probability of getting a number larger than 4 on both throws
To calculate the probability of getting a number larger than 4 on both throws of a six-sided die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are two ways we can approach this problem:
1. **Using the Counting Method**:
- Begin by listing all the possible outcomes of tossing a six-sided die twice. Since each throw has six possible outcomes (numbers 1-6), the total number of outcomes for the two throws will be 6 * 6 = 36.
- Next, identify the number of favorable outcomes, i.e., the cases where you get a number larger than 4 on both throws. These outcomes are:
* Number larger than 4 on the first throw: 5 and 6.
* Number larger than 4 on the second throw: 5 and 6.
- You could count these outcomes mentally, but it's easier to see them by organizing them in a table:
| 1 | 2 | 3 | 4 | **5** | **6** |
----------------------------------
**1** | . | | | | . | . |
**2** | . | | | | . | . |
**3** | . | | | | . | . |
**4** | . | | | | . | . |
**5** | . | | | | . | . |
**6** | . | | | | . | . |
- The dots (.) indicate the unfavorable outcomes, while the highlighted numbers (5 and 6) represent the favorable outcomes.
- Counting the favorable outcomes, we have 2 * 2 = 4.
- Finally, calculate the probability by dividing the number of favorable outcomes by the total number of outcomes: 4 / 36 = 1 / 9 ≈ 0.1111 (rounded to four decimal places).
2. **Using Probability Rules**:
- We can also calculate the probability of each throw separately and then multiply them together.
- The probability of getting a number larger than 4 on a single throw of a six-sided die is 2 / 6 = 1 / 3, as there are 2 favorable outcomes (numbers 5 and 6) out of 6 total outcomes.
- Since the two throws are independent events, we can multiply their probabilities: (1/3) * (1/3) = 1/9 ≈ 0.1111 (rounded to four decimal places).
So, the probability of getting a number larger than 4 on both throws is 1/9, or approximately 0.1111.
To find the probability of getting a number larger than 4 on both throws of a six-sided die, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of possible outcomes.
When a six-sided die is tossed twice, each throw has 6 possible outcomes. So, the total number of possible outcomes is 6 * 6 = 36.
Step 2: Determine the number of favorable outcomes.
To get a number larger than 4 on both throws, we need to consider the possibilities of getting 5 or 6 on each throw. There are 2 favorable outcomes for each throw. Therefore, the number of favorable outcomes is 2 * 2 = 4.
Step 3: Calculate the probability.
The probability of an event is defined as the number of favorable outcomes divided by the number of possible outcomes.
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 36
= 1 / 9
So, the probability of getting a number larger than 4 on both throws of a six-sided die is 1/9.
Probability of rolling a 5 or a 6
P(5,6)=2/6
Probability of rolling a 5 or a 6 twice
=P(5,6)²
= 1/9