Question

9/17/2025 siswojo, jayden

• probability •

solve the following using any method.
a bag has 2 red marbles, 3 blue marbles, and 1 green marble, and a spinner has 3 options. you randomly pull one marble then spin the spinner once.
what is the probability of:

1. pulling a green marble and spinning a 3?
2. pulling a blue marble and spinning an odd number?
3. not pulling a red marble and not spinning a 1?
4. pulling a black marble and spinning a number less than 4?

a regular die has 6 sides and a spinner has 5 options. you spin the spinner once and roll the die once.
what is the probability of getting:

1. orange and a 4?
2. blue or red and a 7?
3. yellow or green and an odd number?
4. a number greater than 4 and a color which is neither green nor blue?

Explanation:

Step1: Calculate total number of marble - spinner combinations

The total number of marbles is $2 + 3+1=6$, and the spinner has 3 options. So the total number of combined outcomes is $6\times3 = 18$.

Step2: Solve part 1

The probability of pulling a green marble is $\frac{1}{6}$ (since there is 1 green marble out of 6), and the probability of spinning a 3 is $\frac{1}{3}$. Using the multiplication - rule for independent events $P(A\cap B)=P(A)\times P(B)$, we have $P=\frac{1}{6}\times\frac{1}{3}=\frac{1}{18}$.

Step3: Solve part 2

The probability of pulling a blue marble is $\frac{3}{6}=\frac{1}{2}$, and the probability of spinning an odd number (1 or 3) is $\frac{2}{3}$. So $P=\frac{1}{2}\times\frac{2}{3}=\frac{1}{3}$.

Step4: Solve part 3

The probability of not pulling a red marble is $\frac{3 + 1}{6}=\frac{4}{6}=\frac{2}{3}$, and the probability of not spinning a 1 is $\frac{2}{3}$. Then $P=\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}$.

Step5: Solve part 4

The probability of pulling a black marble is 0 (since there are no black marbles), so $P = 0\times1=0$ (probability of spinning a number less than 4 is 1 as all 3 numbers on the spinner are less than 4).

Step6: Calculate new total number of spinner - die combinations

The spinner has 5 options and the die has 6 sides, so the total number of combined outcomes is $5\times6 = 30$.

Step7: Solve part 5

The probability of getting orange on the spinner is $\frac{1}{5}$, and the probability of getting a 4 on the die is $\frac{1}{6}$. So $P=\frac{1}{5}\times\frac{1}{6}=\frac{1}{30}$.

Step8: Solve part 6

The probability of getting blue or red on the spinner is $\frac{2}{5}$, and the probability of getting a 7 on the die is 0. So $P=\frac{2}{5}\times0 = 0$.

Step9: Solve part 7

The probability of getting yellow or green on the spinner is $\frac{2}{5}$, and the probability of getting an odd number on the die is $\frac{3}{6}=\frac{1}{2}$. So $P=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}$.

Step10: Solve part 8

The probability of getting a number greater than 4 on the die (5 or 6) is $\frac{2}{6}=\frac{1}{3}$, and the probability of getting a color that is neither green nor blue (orange, red, yellow) on the spinner is $\frac{3}{5}$. So $P=\frac{1}{3}\times\frac{3}{5}=\frac{1}{5}$.

Answer:

1. $\frac{1}{18}$
2. $\frac{1}{3}$
3. $\frac{4}{9}$
4. 0
5. $\frac{1}{30}$
6. 0
7. $\frac{1}{5}$
8. $\frac{1}{5}$