Question

learning goals from lesson 5.1
✓ i can find sample spaces, theoretical probabilities, and experimental probabilities. (standards: s.cp.1, s.md.6+)

1. at a school festival, a colored chip is randomly drawn out of a bag and replaced. the table below shows the results of 75 draws. estimate the probability of choosing a green chip.

outcome	blue	red	green	purple	gold

a. 16%
b. 21.3%
c. 18.7%
d. 32%

Explanation:

Step1: Recall experimental probability formula

Experimental probability of an event is the number of times the event occurs divided by the total number of trials. So, for green chips, it's $\frac{\text{Number of green draws}}{\text{Total number of draws}}$.

Step2: Calculate total number of draws

Sum the draws for all colors: $18 + 14 + 16 + 8 + 19$. Let's compute that: $18+14=32$, $32+16=48$, $48+8=56$, $56+19=75$. So total draws are 75.

Step3: Calculate probability for green

Number of green draws is 16. So probability is $\frac{16}{75}$. Let's compute that as a percentage: $\frac{16}{75} \approx 0.2133$, which is $0.2133 \times 100 \approx 21.3\%$? Wait, no, wait: Wait, 16 divided by 75: 16÷75≈0.2133? Wait, no, 16/75 is approximately 0.2133? Wait, no, 75×0.2133≈16. So 16/75≈0.2133, which is 21.3%? Wait, but let's check again. Wait, 16 divided by 75: 75×0.213 = 15.975, which is close to 16. So the probability is approximately 21.3%, which is option b? Wait, but wait, the options are a.16%, b.21.3%, c.18.7%, d.32%. Wait, 16/75 is approximately 0.213, so 21.3%, so option b.

Answer:

b. 21.3%