1. What is the theoretical probability of rolling a sum less than 5 using two number cubes?
a.1/6
b.1/4
c.1/2
d.3/4
2. Segments parallel to the sides are used to divide a square board 3 ft on each side into 9 equal-size smaller squares. If the board is in a level position and a grain of rice lands on the board at a random point, what is the probability that it lands on a corner section?
a.2/9
b.1/3
c.4/9
d.5/9
For #1 I think the answer is c.1/2 because 2 die=12 so 1+1,1+2,1+3,2+1,2+2,3+1=6(sets). so 6/12=1/2. For the second one, I'm not even sure what the question is asking. Any help would be really helpful. If you could include an explanation that would be great. I don't just want an answer, I want to be able to understand how to do this kinds of problems correctly.
1. But there are 36 combinations for two dice. 6/36 = ?
2. There are nine squares and only 4 corners. What does that tell you?
1. To find the theoretical probability of rolling a sum less than 5 using two number cubes, we need to determine the number of favorable outcomes (combinations that result in a sum less than 5) and the total number of possible outcomes.
First, let's determine the favorable outcomes:
- The possible outcomes for rolling a single number cube are 1, 2, 3, 4, 5, and 6.
- To get a sum less than 5, we can have the following combinations:
- 1+1 = 2
- 1+2 = 3
- 1+3 = 4
- 2+1 = 3
- 2+2 = 4
- 3+1 = 4
This gives us a total of 6 favorable outcomes.
Next, let's determine the total number of possible outcomes:
- Since we're rolling two number cubes, each cube has 6 possible outcomes.
- The total number of possible outcomes will be the product of the number of outcomes for each cube, which is 6 x 6 = 36.
Finally, we can calculate the theoretical probability by dividing the number of favorable outcomes by the total number of possible outcomes:
- Probability = favorable outcomes / total possible outcomes
- Probability = 6 / 36
- Probability = 1/6
Therefore, the correct answer is a. 1/6.
2. The question is asking for the probability that a grain of rice lands on a corner section of a square board divided into 9 equal-size smaller squares.
To solve this problem, we need to determine the total number of corner sections and the total number of possible landing points.
- Since the square board is divided into 9 equal-size smaller squares, each with its own corner, there are 4 corners in each smaller square.
- So, the total number of corner sections on the board will be 4 x 9 = 36.
- The total number of possible landing points on the board is determined by the total number of squares it is divided into. In this case, the board is divided into 9 smaller squares.
Finally, we can calculate the probability by dividing the number of corner sections by the total number of possible landing points on the board:
- Probability = number of corner sections / total possible landing points
- Probability = 36 / 9
- Probability = 4/9
Therefore, the correct answer is c. 4/9.