Will award 50 points & the brainiest answer

1. one spinner has three equally sized sectors labeled r, s, and t. a second spinner has two equally sized sectors labeled 3 and 5. each spinner is spun once. what is the sample space of outcomes?
{rst, 35}
{rr, rs, rt, sr, ss, st, tr, ts, tt, 33, 35, 53, 55}
{r, s, t, 3, 5}
{r3, r5, s3, s5, t3, t5} (my guess)

2. a spinner with three equal sectors is spun three times. what is the number of possible outcomes?
3
6
9
27

3. there are two spinners. the first spinner has three equal sectors labeled 1, 2 and 3. the second spinner has four equal sectors labeled 3, 4, 5 and 6. the spinners are spun once. what is the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner?
2
6
9
12

4. which events are independent?
select each correct answer.

a six-sided number cube is rolled and a coin is flipped.
two spinners are spun at the same time.
one coin is drawn from a bag of coins after another coin is drawn without replacement.
two white balls are drawn from a bag of balls without replacing the balls.

5. ten slips of paper labeled from 1 to 10 are placed in a hat. the first slip of paper is not replaced before selecting the second slip of paper.

what is the probability of selecting a multiple of 3 and then a multiple of 4?

1/15

1/10

3/50

2/45

6. a spinner has 8 equal sectors labeled from 1 to 8. the spinner is spun twice.

what is the probability of getting an even number on the first spin and another even number on the second spin?

1/4

3/16

7/8

5/16

7. a and b are two events.

given that p(a)=0.2 , p(b)=0.3 and p(a and b)=0.06 .

determine if they're independent or dependent.

8. a group of children were asked if they like eating cupcakes or brownies.

the table shows the probabilities of the results.

like cupcakes do not like cupcakes total
like brownies 0.15 0.15 0.3
do not like brownies 0.35 0.35 0.7
total 0.5 0.5 1

which statement is true?

liking cupcakes and brownies are independent since p(cupcakes|brownies) = p(cupcakes) and p(brownies|cupcakes) = p(brownies) .

liking cupcakes and brownies are not independent since p(cupcakes|brownies) = p(cupcakes) .

liking brownies and cupcakes are not independent since p(cupcakes|brownies) ≠ p(cupcakes) and p(brownies|cupcakes) ≠ p(brownies)

liking cupcakes and brownies are independent since p(cupcakes|brownies) = p(brownies) and p(brownies|cupcakes) = p(cupcakes) .

9. which statement best explains conditional probability and independence?

when two separate events, a and b, are independent, p(b|a)=p(a and b)p(a)=p(a)⋅p(b)p(a)=p(b) . this means that the occurrence of event a first did not affect the probability of event b occurring next.

when two separate events, a and b, are independent, p(b|a)=p(a and b)p(a)=p(a)⋅p(b)p(a)=p(b) . this means that the occurrence of event b first did not affect the probability of event a occurring next.

when two separate events, a and b, are independent, p(b|a)=p(a and b)p(a)=p(a)⋅p(b)p(a)=p(b) . this means that the occurrence of event a first affected the probability of event b occurring next.

when two separate events, a and b, are independent, p(b|a)=p(a and b)p(a)=p(a)⋅p(b)p(a)=p(b) . this means that the occurrence of event b first affected the probability of event a occurring next.

10. the probability of choosing two green balls without replacement is 1150 , and the probability of choosing one green ball is 1225 .

what is the probability of drawing a second green ball, given that the first ball is green?

7/10

11/24

66/625

11/12

11. john has a spinner with eight equal sectors with labels from 1 to 8. he spins the spinner once.

what is the probability that he gets a number less than 4 or a multiple of 4?

34

58

332

12

12. a spinner has ten equal sectors labeled from 1 to 10. the spinner is spun once.

what is the probability of getting an odd number and a number greater than 4?

7/10

1/2

3/10

4/5