Pintu thrown two dices simultaneously what is the probability that at least one of them shows a number greater than three . List the outcomes

To solve this problem, let's first consider the total number of possible outcomes when two dice are thrown.

### Total Possible Outcomes:
Each die has 6 faces, so when two dice are thrown, the total number of possible outcomes is:

\[
6 \times 6 = 36
\]

### Favorable Outcomes:
Now, we need to find the probability that at least one die shows a number greater than 3. The numbers greater than 3 on a die are 4, 5, and 6. We can count the outcomes where at least one die shows a 4, 5, or 6.

#### Case 1: First die shows 4, 5, or 6:
- If the first die shows 4, 5, or 6, the second die can show any of the 6 numbers (1, 2, 3, 4, 5, or 6).
- So, there are \(3 \times 6 = 18\) favorable outcomes.

#### Case 2: Second die shows 4, 5, or 6 (and the first die shows a number less than or equal to 3):
- If the second die shows 4, 5, or 6 and the first die shows 1, 2, or 3.
- So, there are \(3 \times 3 = 9\) additional favorable outcomes.

Adding these gives \(18 + 9 = 27\) favorable outcomes.

### Probability:
The probability that at least one die shows a number greater than 3 is:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{27}{36} = \frac{3}{4}
\]

### List of Favorable Outcomes:
The favorable outcomes where at least one die shows a number greater than 3 are:

\[
(4,1), (4,2), (4,

Explore the probability of rolling two dice and having at least one show a number greater than three. Understand the concept of total outcomes and favorable outcomes in probability calculations. Suitable for Grades 7-9.

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