which of the following sample spaces correctly lists all the possible outcomes for flipping a coin and spinning a four-colored spinner (red, blue, green, and yellow)?
A. h-red, h-blue, h-green, h-yellow, t-yellow, i-green, t-blue, t-red
B. h-red, t-red, h-blue, t-blue, h-green, i-yellow
C. t-vellow, h-red, t-blue, h-green, t-green, h-yellow, i-red
D. h-red, t-blue, h-green, t-yellow
The correct answer is option A: h-red, h-blue, h-green, h-yellow, t-yellow, i-green, t-blue, t-red. This correctly lists all the possible outcomes of flipping a coin (heads or tails) and spinning a four-colored spinner (red, blue, green, or yellow).
how many different lunch combinations can be made from two sandwich choices, three side item choices, and three beverage choices if you choose one sandwich, one side, and one beverage?
A. 8
B. 9
C. 18
D.11
The answer is C. 18.
You have 2 choices for the sandwich, 3 choices for the side item, and 3 choices for the beverage. To find the total number of lunch combinations, you multiply the number of options for each category:
2 (sandwich choices) × 3 (side item choices) × 3 (beverage choices) = 18
Therefore, there are 18 different lunch combinations that can be made.
a number cube is rolled. what is p(3 or an even number)?
A. 1/2
B. 2/3
C. 4/2
D. 1/6
The answer is B. 2/3.
To find the probability of rolling a 3 or an even number on a number cube, you need to add the probability of rolling a 3 and the probability of rolling an even number (2, 4, or 6). However, you need to make sure that you are not counting the number 6 twice (since it is both even and a multiple of 3).
The probability of rolling a 3 is 1/6.
The probability of rolling an even number is 3/6 (since there are three even numbers out of six total numbers on the cube). However, we need to subtract the probability of rolling a 6, since it is both even and a multiple of 3. The probability of rolling a 6 is 1/6, so the probability of rolling an even number that is not 6 is 2/6.
Therefore, the probability of rolling a 3 or an even number is:
P(3 or even) = P(3) + P(even) - P(3 and even)
P(3 or even) = 1/6 + 2/6 - 1/6
P(3 or even) = 2/6 or 1/3
This can be simplified to 2/3. Therefore, the answer is B.
which of the following is a certain event?
A certain event is an event that will always happen, with probability 1. In other words, it is guaranteed to occur.
Out of the list of options you did not provide, but an example of a certain event is:
- Rolling a standard six-sided die and getting a number between 1 and 6.
This is a certain event because it is impossible to roll a number that is not between 1 and 6 on a standard six-sided die.
which of the following is a certain event?
A. rolling a composite number on a number cube
B. rolling a number greater than 1 on a number cube
C. rolling an odd or even number on a number cube
D. rolling an odd or even number greater than 7
The answer is B. rolling a number greater than 1 on a number cube.
A certain event is an event that will always happen, with probability 1. Rolling a number greater than 1 on a standard six-sided die is a certain event, since all of the numbers on the die are greater than 1.
Rolling a composite number (option A) is not a certain event, since half of the numbers on the die (2 and 3) are prime and the other half are composite.
Rolling an odd or even number (option C) is not a certain event either, since it is possible to roll a number that is neither odd nor even (such as 1).
Rolling an odd or even number greater than 7 (option D) is impossible, since the largest number on a standard six-sided die is 6, which is not greater than 7.
a class has 9 girls and 12 boys. what is the probability of a teacher randomly calling on a boy?
A. 3/4
B. 4/7
C. 3/7
D. 4/3