James used a table to determine the sample space for an experiment in which a purple (P) or yellow (Y) marble is selected from a bag 4 times and replaced after each draw.
Row 1 PPPP PPPY PPPY PPYP
Row 2 PYPP YPPP PYPY YPYP
Row 3 YYYY YYYP YYPY YPYY
Row 4 PYYY YYPP PPYY PYYP
In which row did James make an error when he created his table? Answer 1 for row 1, 2 for row 2, 3 for row 3, or 4 for row 4.
James made an error in Row 3.
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 denote the outcomes of each roll as follows:
1st roll: {1, 2, 3, 4, 5, 6, 7, 8}
2nd roll: {1, 2, 3, 4, 5, 6, 7, 8}
The sample space for rolling an eight-sided number cube twice is as follows:
1st Roll 2nd Roll
1 1
1 2
1 3
1 4
1 5
1 6
1 7
1 8
2 1
2 2
2 3
2 4
2 5
2 6
2 7
2 8
3 1
3 2
3 3
3 4
3 5
3 6
3 7
3 8
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
5 1
5 2
5 3
5 4
5 5
5 6
5 7
5 8
6 1
6 2
6 3
6 4
6 5
6 6
6 7
6 8
7 1
7 2
7 3
7 4
7 5
7 6
7 7
7 8
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 8
There are a total of 64 different possible outcomes when rolling an eight-sided number cube twice.
Use the image to answer the question.
An illustration of a circle with four equal differently colored parts labeled 1, 2, 3, 4 clockwise. An arrow starting at the center points toward 1.
The spinner is spun twice. What is the probability of spinning orange (dots) on both spins? Express your answer as a simplified fraction.
If the spinner has orange dots only in section 1, and we want to find the probability of spinning orange on both spins, then the probability is (1/4) * (1/4) = 1/16.
Therefore, the probability of spinning orange on both spins is 1/16.
Use the image to answer the question.
An illustration of a circle with four equal differently colored parts labeled 1, 2, 3, 4 clockwise. An arrow starting at the center points toward 1.
The spinner is spun twice. What is the probability of spinning an even number on both spins? Express your answer as a simplified fraction.
Since the spinner has numbers 1, 2, 3, 4, and we want to find the probability of spinning an even number on both spins, the possible even numbers are 2 and 4.
The total number of outcomes for each spin is 4 (1, 2, 3, 4).
The probability of spinning an even number on the first spin is 2/4 = 1/2.
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.
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.
When a traditional number cube is rolled, it has six faces numbered 1 through 6.
For the first roll to land on an even number, the possible outcomes are 2, 4, or 6. So, the probability of the first roll landing on an even number is 3/6 or 1/2.
For the second roll to land on an odd number, the possible outcomes are 1, 3, or 5. So, the probability of the second roll landing on an odd number is 3/6 or 1/2.
The probability of the first roll being even and the second roll being odd is the product of the two probabilities:
P(first roll even and second roll odd) = (1/2) * (1/2) = 1/4.
Therefore, the probability that the first roll lands on an even number and the second roll lands on an odd number is 1/4.