determine whether each pair of actions results in independent or dependent events.
1. pick one marble out of a bag. then, without replacing the marble, pick another marble.
a. dependent; the first marble selection will affect the second marble selection.
b. independent; the first marble selection will not affect the second marble selection.
c. dependent; the first marble selection will not affect the second marble selection.
d. independent; the first marble selection will affect the second marble selection.
2. toss a coin. then spin the pointer of a spinner.
a. independent; the coin toss will affect the spinner result.
b. dependent; the coin toss will affect the spinner result.
c. dependent; the coin toss will not affect the spinner result.
d. independent; the coin toss will not affect the spinner result.
3. you roll a standard number cube. find ( p( ext{number is not } 3) ).
a. ( \frac{2}{3} )
b. ( \frac{1}{6} )
c. ( \frac{1}{2} )
d. ( \frac{5}{6} )
4. a drug trial is testing the effectiveness of two drugs. if 50 patients are given drug a, 20 patients are given drug b, and 100 patients are given a placebo, what is the probability that a patient will not be given a placebo?
a. ( \frac{5}{17} )
b. ( \frac{10}{17} )
c. ( \frac{2}{17} )
d. ( \frac{7}{17} )
5. suppose ( s ) and ( t ) are mutually exclusive events, ( p(s) = 20% ), and ( p(t) = 22% ). find ( p(s ext{ or } t) ).
a. ( 2% )
b. ( 440% )
c. ( 42% )
d. ( 4.4% )
6. a jar contains 2 blue cubes, 5 blue spheres, 2 green cubes, and 5 green spheres. if you select an object at random, what is the probability that the object is green or a cube?

Question

determine whether each pair of actions results in independent or dependent events.
1. pick one marble out of a bag. then, without replacing the marble, pick another marble.
a. dependent; the first marble selection will affect the second marble selection.
b. independent; the first marble selection will not affect the second marble selection.
c. dependent; the first marble selection will not affect the second marble selection.
d. independent; the first marble selection will affect the second marble selection.
2. toss a coin. then spin the pointer of a spinner.
a. independent; the coin toss will affect the spinner result.
b. dependent; the coin toss will affect the spinner result.
c. dependent; the coin toss will not affect the spinner result.
d. independent; the coin toss will not affect the spinner result.
3. you roll a standard number cube. find ( p(	ext{number is not } 3) ).
a. ( \frac{2}{3} )
b. ( \frac{1}{6} )
c. ( \frac{1}{2} )
d. ( \frac{5}{6} )
4. a drug trial is testing the effectiveness of two drugs. if 50 patients are given drug a, 20 patients are given drug b, and 100 patients are given a placebo, what is the probability that a patient will not be given a placebo?
a. ( \frac{5}{17} )
b. ( \frac{10}{17} )
c. ( \frac{2}{17} )
d. ( \frac{7}{17} )
5. suppose ( s ) and ( t ) are mutually exclusive events, ( p(s) = 20% ), and ( p(t) = 22% ). find ( p(s 	ext{ or } t) ).
a. ( 2% )
b. ( 440% )
c. ( 42% )
d. ( 4.4% )
6. a jar contains 2 blue cubes, 5 blue spheres, 2 green cubes, and 5 green spheres. if you select an object at random, what is the probability that the object is green or a cube?

Accepted Answer

### Question 1
# Explanation:
## Step1: Recall independent/dependent events
Independent events: one event doesn't affect the other. Dependent events: one event affects the other.
## Step2: Analyze marble selection
When we pick a marble without replacement, the first pick changes the number of marbles left, so the first selection affects the second. So it's dependent. Option A says dependent and explains the first affects the second, which matches.
# Answer: A. Dependent; the first marble selection will affect the second marble selection.

### Question 2
# Explanation:
## Step1: Recall independent/dependent events
Coin toss and spinner spin: the result of a coin toss doesn't affect the spinner's result. So they are independent.
## Step2: Match with options
Option D says independent and that the coin toss doesn't affect the spinner result, which is correct.
# Answer: D. Independent; the coin toss will not affect the spinner result.

### Question 3
# Explanation:
## Step1: Determine total outcomes
A standard number cube has 6 faces (numbers 1 - 6).
## Step2: Determine favorable outcomes
"Not 3" means numbers 1,2,4,5,6. So 5 favorable outcomes.
## Step3: Calculate probability
Probability $ P = \frac{\text{favorable}}{\text{total}} = \frac{5}{6} $.
# Answer: D. $\frac{5}{6}$

### Question 4
# Explanation:
## Step1: Calculate total number of patients
Patients with Drug A: 50, Drug B: 20, placebo: 100. Total $ = 50 + 20 + 100 = 170 $.
## Step2: Calculate number of patients not given placebo
Not placebo means Drug A + Drug B $ = 50 + 20 = 70 $.
## Step3: Calculate probability
Probability $ P = \frac{70}{170} = \frac{7}{17} $.
# Answer: D. $\frac{7}{17}$

### Question 5
# Explanation:
## Step1: Recall formula for mutually exclusive events
For mutually exclusive events, $ P(S \text{ or } T) = P(S) + P(T) $.
## Step2: Substitute values
$ P(S) = 20\% = 0.2 $, $ P(T) = 22\% = 0.22 $. So $ P(S \text{ or } T) = 0.2 + 0.22 = 0.42 = 42\% $.
# Answer: C. 42%

### Question 6
# Explanation:
## Step1: Determine total number of objects
Blue cubes: 2, blue spheres: 5, green cubes: 2, green spheres: 5. Total $ = 2 + 5 + 2 + 5 = 14 $.
## Step2: Use inclusion - exclusion principle for "green or cube"
Let $ G $ be green, $ C $ be cube. $ P(G \text{ or } C) = P(G) + P(C) - P(G \text{ and } C) $.
- $ P(G) $: green objects are $ 2 + 5 = 7 $, so $ P(G)=\frac{7}{14} $.
- $ P(C) $: cube objects are $ 2 + 2 = 4 $, so $ P(C)=\frac{4}{14} $.
- $ P(G \text{ and } C) $: green cubes are 2, so $ P(G \text{ and } C)=\frac{2}{14} $.
## Step3: Calculate the probability
$ P(G \text{ or } C)=\frac{7}{14}+\frac{4}{14}-\frac{2}{14}=\frac{7 + 4-2}{14}=\frac{9}{14} $ (Wait, let's re - check the counts:
Blue cubes: 2, blue spheres: 5, green cubes: 2, green spheres: 5. Total objects: $ 2 + 5+2 + 5=14 $.
Green objects: green cubes (2) + green spheres (5) = 7.
Cube objects: blue cubes (2)+green cubes (2) = 4.
Green and cube: green cubes = 2.
So $ P(G\cup C)=P(G)+P(C)-P(G\cap C)=\frac{7}{14}+\frac{4}{14}-\frac{2}{14}=\frac{9}{14}\approx0.6429 $. But let's do it step by step:
Number of green or cube: green (7) + cube (4) - green and cube (2) = 9. So probability $=\frac{9}{14}$. Wait, but maybe I made a mistake. Wait, blue cubes: 2, blue spheres: 5, green cubes: 2, green spheres: 5. So:
- Green objects: 2 (cubes) + 5 (spheres) = 7.
- Cube objects: 2 (blue) + 2 (green) = 4.
- Green and cube: 2 (green cubes).
So using inclusion - exclusion, the number of elements in $ G\cup C $ is $ 7 + 4-2 = 9 $. Total elements 14. So probability is $ \frac{9}{14} $. But let's check the options (if there were options, but since the question is to solve it, we can present the answer as $ \frac{9}{14} $ or simplify. Wait, maybe I miscalculated total? Wait 2 + 5 is 7 (blue), 2+5 is 7 (green), total 14. Yes. So green or cube: 9 out of 14. So $ P=\frac{9}{14}$.
# Answer: $\frac{9}{14}$ (or approximately 0.643)

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QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Recall independent/dependent events

Step2: Analyze marble selection

Step1: Recall independent/dependent events

Step2: Match with options

Step1: Determine total outcomes

Step2: Determine favorable outcomes

Step3: Calculate probability

Answer:

Question 2