If dennis rolls 2 number cubes with sides labeled 1 to 6, what is the probability that the sum of the numbers is greater than or equal to 10?
daniela flipped a coin and spun a spinner that is divided into four equal- size sectors colored red, yellow, green, and orange. Write the sample space of all possible outcomes
## 1 2 3 4 5 6
1
2
3
4 - - - - - *
5 - - - - * *
6 - - - * * *
looks like 6/36 = 1/6
heads , p = .5 then r y g o
tails, p = .5, then r g y o
probability of each outcome = 1/2 * 1/4 = 1/8
Joy rolls 2 number cubes at the same time that each have sides labeled 1 to 6. What is the probability that the sum of the numbers will be greater than or equal to 5?
To find the probability that the sum of the numbers rolled on two number cubes is greater than or equal to 10, we need to determine the total number of favorable outcomes and divide it by the total number of possible outcomes.
Let's first find the total number of possible outcomes. Each number cube has 6 sides, so the first cube can land on any of the six numbers, and similarly, the second cube can also land on any of the six numbers. The total number of possible outcomes is given by multiplying the number of possible outcomes for each cube, which is 6 x 6 = 36.
To determine the favorable outcomes, we need to find the pairs of numbers whose sum is greater than or equal to 10. We can list them out:
(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)
There are six favorable outcomes in total.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 36
= 1 / 6
≈ 0.1667
Therefore, the probability that the sum of the numbers rolled on the two number cubes is greater than or equal to 10 is approximately 0.1667 or 1/6.
Now, let's move on to the second question about Daniela's coin flip and spinner spin.
For the coin flip, there are two possible outcomes: heads or tails.
For the spinner spin, there are four possible outcomes: red, yellow, green, and orange.
To determine the sample space of all possible outcomes when combining the coin flip and spinner spin, we need to consider each outcome from the coin flip with each outcome from the spinner spin.
So, the sample space consists of all possible combinations:
{heads, red}, {heads, yellow}, {heads, green}, {heads, orange},
{tails, red}, {tails, yellow}, {tails, green}, {tails, orange}
The sample space consists of eight possible outcomes.
Therefore, the sample space of all possible outcomes for Daniela's coin flip and spinner spin is {heads, red}, {heads, yellow}, {heads, green}, {heads, orange}, {tails, red}, {tails, yellow}, {tails, green}, {tails, orange}.