Question

amanda will spin this spinner once. what is the probability that she will not spin a number less than 4? options: \\(\frac{1}{3}\\), \\(\frac{2}{3}\\), \\(\frac{3}{7}\\), \\(\frac{4}{7}\\)

Explanation:

Step1: Count total sections

The spinner has 6 sections (numbers 2,3,4,5,6,7).

Step2: Identify numbers ≥4

Numbers not less than 4 (i.e., ≥4) are 4,5,6,7. So there are 4 such numbers.

Step3: Calculate probability

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$ = $\frac{4}{6}$ = $\frac{2}{3}$. Wait, wait, no—wait, the spinner: let's recheck. Wait, the spinner has 6 sections? Wait, looking at the spinner: colors are green (7), yellow (2), green (3), purple (4), blue (5), orange (6). So total 6 sections? Wait, no, wait the numbers: 2,3,4,5,6,7. So 6 numbers. Wait, but the options have denominators 3 and 7. Wait, maybe I miscounted. Wait, let's look again. The spinner: the sections are 7 (green), 2 (yellow), 3 (green), 4 (purple), 5 (blue), 6 (orange). Wait, that's 6 sections? But the options have 3 and 7. Wait, maybe the spinner has 6 sections? Wait, no, maybe I made a mistake. Wait, the numbers are 2,3,4,5,6,7—six numbers. Wait, but the options: 1/3, 2/3, 3/7, 4/7. Wait, maybe the spinner has 6 sections? Wait, 6 sections: numbers 2,3,4,5,6,7. Numbers less than 4: 2,3 (two numbers). So numbers not less than 4: 4,5,6,7 (four numbers). So probability is 4/6 = 2/3. Ah, 4/6 simplifies to 2/3. So the correct answer is 2/3.

Answer:

$\frac{2}{3}$ (corresponding to the option with $\frac{2}{3}$)