Question

a bag contains red, blue, green, and yellow tokens. a token is selected at random and then replaced. this process is performed 2,000 times. the results are given.

• red tokens: 605
• blue tokens: 342
• green tokens: 518
• yellow tokens: 535

based on the data, which fraction is closest to the probability of randomly selecting a red token?
a $\frac{1}{4}$
b $\frac{3}{10}$
c $\frac{9}{20}$
d $\frac{7}{10}$

Explanation:

Step1: Calculate the probability of red tokens

The probability of selecting a red token is the number of red token selections divided by the total number of selections. So we have $\frac{605}{2000}$.

Step2: Simplify and compare with options

Simplify $\frac{605}{2000} = 0.3025$. Now check the options:

• Option A: $\frac{1}{4}=0.25$
• Option B: $\frac{3}{10}=0.3$
• Option C: $\frac{9}{20}=0.45$
• Option D: $\frac{7}{10}=0.7$

The value $0.3025$ is closest to $0.3$ (which is $\frac{3}{10}$). But wait, wait, $605\div2000 = 0.3025$, and $\frac{9}{20}=0.45$, $\frac{3}{10}=0.3$, $\frac{1}{4}=0.25$, $\frac{7}{10}=0.7$. Wait, 0.3025 is closer to 0.3 (3/10) or 0.25 (1/4)? Wait 0.3025 - 0.25 = 0.0525, 0.3025 - 0.3 = 0.0025. Oh, I made a mistake earlier. So 0.3025 is closer to 0.3 (3/10)? Wait no, 0.3025 - 0.3 = 0.0025, and 0.3025 - 0.25 = 0.0525. So it's closer to 0.3 (3/10)? Wait but wait, 605/2000 = 121/400 = 0.3025. Wait, 3/10 is 0.3, 9/20 is 0.45. Wait, 0.3025 is 0.3025, so the difference between 0.3025 and 0.3 is 0.0025, and between 0.3025 and 0.25 is 0.0525, between 0.3025 and 0.45 is 0.1475. So the closest is 3/10? Wait no, wait the options: A is 1/4 (0.25), B is 3/10 (0.3), C is 9/20 (0.45), D is 7/10 (0.7). So 0.3025 is closest to 0.3 (3/10) because 0.3025 - 0.3 = 0.0025, which is very small. Wait but wait, 605 divided by 2000: 2000 divided by 4 is 500, 605 is 105 more than 500. Wait, maybe I miscalculated. Wait 605/2000: let's simplify 605 and 2000. Divide numerator and denominator by 5: 121/400. 121 divided by 400 is 0.3025. Now, 3/10 is 0.3, 9/20 is 0.45. So 0.3025 is 0.3025, so the difference between 0.3025 and 0.3 is 0.0025, and between 0.3025 and 0.25 is 0.0525. So the closest is 3/10 (0.3). But wait, the option B is 3/10, option A is 1/4. Wait, but let's check again. Wait 605 is the number of red tokens, total trials 2000. So probability is 605/2000 = 0.3025. Now, 3/10 is 0.3, 9/20 is 0.45. So 0.3025 is very close to 0.3 (3/10). So the answer should be B? Wait no, wait 9/20 is 0.45, which is 0.45, 0.3025 is 0.3025, so the difference between 0.3025 and 0.3 is 0.0025, and between 0.3025 and 0.45 is 0.1475, between 0.3025 and 0.25 is 0.0525. So the closest is 3/10 (0.3). So the answer is B? Wait but wait, maybe I made a mistake. Wait 605 divided by 2000: 2000 times 0.3 is 600, so 605 is 5 more than 600, so 605/2000 = 0.3025, which is 0.3025, so the fraction closest is 3/10 (0.3) because 0.3025 - 0.3 = 0.0025, which is very small. So the answer is B? Wait no, wait the options: A is 1/4 (0.25), B is 3/10 (0.3), C is 9/20 (0.45), D is 7/10 (0.7). So the correct answer is B? Wait, but let's check again. 605/2000 = 0.3025. The difference between 0.3025 and 0.3 (3/10) is 0.0025, and between 0.3025 and 0.25 (1/4) is 0.0525. So yes, closest to 3/10. Wait but wait, the problem says "which fraction is closest". So 3/10 is 0.3, 1/4 is 0.25, 9/20 is 0.45. So 0.3025 is closest to 0.3 (3/10). So the answer is B.

Answer:

B. $\frac{3}{10}$