spinner: 1 (Grey), 2 (Blue), 3 (Green), 4 (Orange)
The spinner is spun twice. What is the probability of spinning an even number on both spins? Express your answer as a simplified fraction.
The even numbers on the spinner are 2 and 4, so the probability of spinning an even number on the first spin is 2/4 = 1/2.
Since the spinner is replaced after each spin, the probability of spinning an even number on the second spin is also 1/2.
Therefore, the probability of spinning an even number on both spins is (1/2) * (1/2) = 1/4.
So, the probability of spinning an even number on both spins is 1/4.
Use a tree diagram or table to determine the sample space for an experiment in which an eight-sided number cube is rolled twice. How many different possible outcomes are there? (
To determine the sample space for rolling an eight-sided number cube twice, we can use a table.
Let's label the outcomes as A, B, C, D, E, F, G, H for the numbers 1 to 8.
| | First Roll | Second Roll |
|-----|------------|-------------|
| Row 1 | A | A |
| Row 2 | A | B |
| Row 3 | A | C |
| Row 4 | A | D |
| Row 5 | A | E |
| Row 6 | A | F |
| Row 7 | A | G |
| Row 8 | A | H |
| Row 9 | B | A |
| ... | ... | ... |
| Row 64 | H | H |
There are 8 possible outcomes for the first roll and 8 possible outcomes for the second roll, so the total number of different possible outcomes is 8 x 8 = 64.
Therefore, there are 64 different possible outcomes when an eight-sided number cube is rolled twice.
spinner: 1 (Grey), 2 (Blue), 3 (Green), 4 (Orange)
The spinner is spun twice. What is the probability of spinning orange on both spins? Express your answer as a simplified fraction.
The probability of spinning orange on the first spin is 1/4 since there is one orange section out of a total of 4 sections.
After the first spin, the spinner is replaced, so the probability of spinning orange on the second spin is also 1/4.
Therefore, the probability of spinning orange on both spins is (1/4) * (1/4) = 1/16.
So, the probability of spinning orange on both spins is 1/16.
A traditional number cube is rolled twice. What is the probability that the first roll lands on an even number, and the second roll lands on an odd number? Express your answer as a simplified fraction. (1 point)
When a traditional number cube is rolled twice, there are 6 possible outcomes for each roll.
For the first roll, the probability of landing on an even number is 3/6 = 1/2, as there are 3 even numbers (2, 4, 6) out of a total of 6 numbers on the cube.
For the second roll, the probability of landing on an odd number is also 3/6 = 1/2, as there are 3 odd numbers (1, 3, 5) out of a total of 6 numbers on the cube.
Therefore, the probability of the first roll landing on an even number and the second roll landing on an odd number is (1/2) * (1/2) = 1/4.
So, the probability that the first roll lands on an even number, and the second roll lands on an odd number is 1/4.