Eduardo has a red 6-sided number cube and a blue 6-sided number cube. The faces of the cubes are numbered 1 through 6.

Eduardo rolls both cubes at the same time.

The random variable X is the number on the red cube minus the number on the blue cube.

What is P(−2≤X≤1)?

I'm thoroughly vexed with this question. It's not covered in my lessons, and I can't get help with a teacher until tomorrow. If anyone can help, I would majorly appreciate it. Thanks. :)

Just list the possibilities. You know there are 36 total outcomes. How many fit the conditions?

R B R-B
1 1 0
1 2 -1
1 3 -2

2 1 1
2 2 0
2 3 -1
2 4 -2
...
4 6 -2

Then divide the successes by the total of 36

20/36

It's 18/36

A sum of money invested at 7.5% per annum amounts to RS 3920 in 3 years. What will it amount to in 2 years 6 months at 9% per annum?

To solve this problem, we need to consider all the possible outcomes when rolling both the red and blue number cubes, and determine the probability of obtaining a result between -2 and 1.

Let's break it down step by step:

1. Determine the possible outcomes: Since both cubes have 6 sides numbered from 1 to 6, there are 6 x 6 = 36 possible outcomes. Each outcome represents a combination of a number on the red cube and a number on the blue cube.

2. Calculate the difference between the number on the red cube and the number on the blue cube for each outcome. Record these differences in a table.

For example:
- If the red cube shows 1 and the blue cube shows 1, the difference is 1 - 1 = 0.
- If the red cube shows 2 and the blue cube shows 1, the difference is 2 - 1 = 1.
- If the red cube shows 1 and the blue cube shows 2, the difference is 1 - 2 = -1.
- If the red cube shows 1 and the blue cube shows 6, the difference is 1 - 6 = -5.

3. Calculate the probabilities for each possible difference. To do so, count the number of times each difference occurs and divide it by the total number of outcomes (36).

Fill in the table with the probabilities for each difference:

| Difference | Probability |
|------------|-------------|
| -5 | ?? |
| -4 | ?? |
| -3 | ?? |
| -2 | ?? |
| -1 | ?? |
| 0 | ?? |
| 1 | ?? |
| 2 | ?? |
| 3 | ?? |
| 4 | ?? |
| 5 | ?? |

4. Calculate the probability of obtaining a result between -2 and 1, inclusive (P(-2 ≤ X ≤ 1)). To do this, sum the probabilities of the differences -2, -1, 0, and 1.

P(-2 ≤ X ≤ 1) = P(X = -2) + P(X = -1) + P(X = 0) + P(X = 1)

Now, you need to calculate the probabilities for each difference and fill in the table.

Once you have the probabilities, you can add up P(X = -2), P(X = -1), P(X = 0), and P(X = 1) to find P(-2 ≤ X ≤ 1).

I hope this explanation helps you solve the problem! Let me know if you have any further questions.