Question

suppose a jar contains 5 red marbles, 4 white marbles, and 3 blue marbles. if a marble is drawn at random from the jar, what is the probability that it is:
⑧ red?
⑨ white?
⑩ blue?
a spinner is pictured at the right. if the arrow is spun, what is the probability that the spinner lands on:
⑪ 2?
⑫ 3?
⑬ 5?
⑭ an even number?
⑮ a number less than 3?
⑯ suppose the arrow is spun 50 times. about how many times would you expect the spinner to land on an odd number?

Explanation:

Step1: Calculate total marbles

Total marbles = $5 + 4 + 3 = 12$

Step2: Probability of red marble

Probability = $\frac{\text{Red marbles}}{\text{Total marbles}} = \frac{5}{12}$

Step3: Probability of white marble

Probability = $\frac{\text{White marbles}}{\text{Total marbles}} = \frac{4}{12} = \frac{1}{3}$

Step4: Probability of blue marble

Probability = $\frac{\text{Blue marbles}}{\text{Total marbles}} = \frac{3}{12} = \frac{1}{4}$

Step5: Probability spinner lands on 2

Spinner has 6 equal sections, 1 section for 2. Probability = $\frac{1}{6}$

Step6: Probability spinner lands on 3

1 section for 3. Probability = $\frac{1}{6}$

Step7: Probability spinner lands on 5

1 section for 5. Probability = $\frac{1}{6}$

Step8: Probability of even number

Even numbers: 2,4 (2 sections). Probability = $\frac{2}{6} = \frac{1}{3}$

Step9: Probability of number <3

Numbers <3: 1,2 (2 sections). Probability = $\frac{2}{6} = \frac{1}{3}$

Step10: Expected odd number spins

Odd numbers: 1,3,5 (3 sections). Probability of odd = $\frac{3}{6} = \frac{1}{2}$. Expected spins = $50 \times \frac{1}{2} = 25$

Answer:

1. $\frac{5}{12}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{1}{6}$
5. $\frac{1}{6}$
6. $\frac{1}{6}$
7. $\frac{1}{3}$
8. $\frac{1}{3}$
9. 25