I have my answers but need them checked and i probably got them wrong so if you can please explain.

#1: 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, T-green, T-blue, T-red
(B) H-red, T-red, H-blue, T-blue, H-green, T-yellow*****
(C) T-yellow, H-red, T-blue, H-green, T-green, H-yellow, T-red
(D) H-red, T-blue, H-green, T-yellow

#2:How many different lunch combinations can be made from two sandwich choices, three side item choices, and three beverage choices if you choose one sandwhich, one side, and one beverage?
(A) 8
(B) 9
(C) 18***
(D) 11

#3: 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

#4: 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

#1

you have 4 colours and 2 ways to flip a coin
so there should be 8 possible outcomes.
your choice has only 6 outcomes

#2, correct
#3, correct
#4, no, there are 21 students, 12 of which are boys
prob = 12/21 = 4/7
you stated the ratio of girls : boys

Thanks Reiny :) You helped me get up to an A in Mathematics :3 Thx -Warrior Cat Lover

#1: To figure out the correct sample space, we need to list all the possible outcomes for flipping a coin and spinning a four-colored spinner. For flipping a coin, we have two possibilities: heads (H) and tails (T). For spinning a four-colored spinner, we have four possibilities: red (R), blue (B), green (G), and yellow (Y).

Now, we need to list all the possible outcomes by combining the coin flip outcomes with the spinner outcomes.

(A) H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red - This sample space includes all the possible outcomes for the coin flip and the spinner, so it is a correct answer.

(B) H-red, T-red, H-blue, T-blue, H-green, T-yellow - This sample space is missing the T-green outcome for the spinner, so it is not correct.

(C) T-yellow, H-red, T-blue, H-green, T-green, H-yellow, T-red - This sample space includes all the possible outcomes for the coin flip and the spinner, so it is a correct answer.

(D) H-red, T-blue, H-green, T-yellow - This sample space is missing the T-green and T-red outcomes for the spinner, so it is not correct.

From the options provided, the correct answer is (A) H-red, H-blue, H-green, H-yellow, T-yellow, T-green, T-blue, T-red.

#2: To find the number of different lunch combinations, we need to multiply the number of choices for each category: sandwich choices, side item choices, and beverage choices.

Given that there are two sandwich choices, three side item choices, and three beverage choices, the number of different lunch combinations can be calculated as 2 * 3 * 3 = 18.

Therefore, the correct answer is (C) 18.

#3: A certain event refers to an event that is guaranteed to happen.

(A) Rolling a composite number on a number cube - This is not a certain event because there is a possibility of rolling a prime number on a number cube.

(B) Rolling a number greater than 1 on a number cube - This is not a certain event because there is a possibility of rolling a 1 on a number cube.

(C) Rolling an odd or even number on a number cube - This is a certain event because every number rolled on a number cube is either odd or even. There is no other possibility.

(D) Rolling an odd or even number greater than 7 - This is not a certain event because rolling a number greater than 7 is not possible on a number cube.

Therefore, the correct answer is (C) Rolling an odd or even number on a number cube.

#4: The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the favorable outcome is the teacher randomly calling on a boy, and the total number of outcomes is the sum of boys and girls in the class (9 girls + 12 boys = 21).

Therefore, the probability of the teacher randomly calling on a boy is calculated as the number of boys (12) divided by the total number of students (21): 12/21, which can be simplified to 4/7.

Therefore, the correct answer is (B) 4/7.