Question

1. you spin a spinner with sections labeled 1 - 15. find the probability of the event: even number.

a) \\( \frac { 1 } { 2 } \\) b) \\( \frac { 8 } { 15 } \\)
c) \\( \frac { 1 } { 3 } \\) d) \\( \frac { 7 } { 15 } \\)

1. you spin a spinner with sections labeled 1 - 15. find the probability of the event: 3 or 4.

a) \\( \frac { 1 } { 15 } \\) b) \\( \frac { 2 } { 15 } \\)
c) \\( \frac { 1 } { 5 } \\) d) \\( \frac { 4 } { 15 } \\)

1. you spin a spinner with sections labeled 1 - 15. find the probability of the event: even number or multiple of 3.

a) \\( \frac { 3 } { 5 } \\) b) \\( \frac { 7 } { 15 } \\)
c) \\( \frac { 1 } { 2 } \\) d) \\( \frac { 2 } { 3 } \\)

1. a bag contains 4 blue marbles, 5 yellow marbles, and 3 red marbles. if you draw one marble at random, find the probability of red.

a) \\( \frac { 1 } { 3 } \\) b) \\( \frac { 3 } { 5 } \\)
c) \\( \frac { 5 } { 12 } \\) d) \\( \frac { 1 } { 4 } \\)

Explanation:

Step1: Determine the total number of outcomes

For spinner problems (questions 1 - 3), the spinner has 15 sections, so the total number of outcomes \(n(S)=15\). For the marble problem (question 4), the total number of marbles \(n = 4 + 5+3=12\).

Step2: Calculate the number of favorable outcomes for each question

• Question 1:

Even numbers from 1 - 15 are \(2,4,6,8,10,12,14\). So \(n(E_1)=7\).

• Question 2:

The event is getting 3 or 4. So \(n(E_2) = 2\).

• Question 4:

The number of red marbles \(n(E_4)=3\).

Step3: Use the probability formula \(P(E)=\frac{n(E)}{n(S)}\)

• Question 1:

\(P(\text{even})=\frac{7}{15}\)

• Question 2:

\(P(3\text{ or }4)=\frac{2}{15}\)

• Question 4:

\(P(\text{red})=\frac{3}{12}=\frac{1}{4}\)

Answer:

1. d) \(\frac{7}{15}\)
2. b) \(\frac{2}{15}\)
3. d) \(\frac{1}{4}\)