Question

you spin the spinner twice.
what is the probability of landing on a number greater than 3 and then landing on a number greater than 5?
write your answer as a fraction or whole number.

Explanation:

Step1: Identify numbers >3

Spinner numbers: 3,4,5,6. Numbers >3: 4,5,6 (3 numbers). Total sections: 4. Probability (first spin): $\frac{3}{4}$.

Step2: Identify numbers >5

Numbers >5: 6 (1 number). Probability (second spin): $\frac{1}{4}$.

Step3: Multiply probabilities (independent events)

Probability = $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$? Wait, no—wait, numbers >3: 4,5,6 (3 numbers), total 4. Numbers >5: only 6 (1 number). Wait, first spin: numbers >3 are 4,5,6 (3 out of 4). Second spin: numbers >5 is 6 (1 out of 4). So multiply: $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$? Wait, no, wait: wait, the spinner has 4 sections: 3,4,5,6. So first, numbers greater than 3: 4,5,6 (three numbers: 4,5,6). So probability first spin: 3/4. Then, numbers greater than 5: only 6 (one number). So probability second spin: 1/4. Then, since spins are independent, multiply: (3/4)(1/4)= 3/16? Wait, no, wait—wait, maybe I made a mistake. Wait, the spinner has 4 equal sections: 3,4,5,6. So first, "number greater than 3": 4,5,6 (3 numbers), so P1 = 3/4. Then, "number greater than 5": only 6 (1 number), so P2 = 1/4. Then, the combined probability is P1 P2 = (3/4)(1/4) = 3/16? Wait, but let's check again. Wait, the spinner has 4 sections: 3 (orange), 4 (blue), 5 (cyan), 6 (purple). So numbers: 3,4,5,6. So numbers greater than 3: 4,5,6 (three numbers). Numbers greater than 5: 6 (one number). So yes, first probability: 3/4, second: 1/4. Multiply: 3/16. So the answer is 3/16? Wait, no, wait—wait, maybe I messed up the first part. Wait, "greater than 3": 4,5,6 are all greater than 3 (since 4>3, 5>3, 6>3). 3 is not. So 3 out of 4. Then "greater than 5": only 6 (since 5 is not greater than 5, 4 and 3 too). So 1 out of 4. So 3/4 1/4 = 3/16. So the answer is 3/16.

Answer:

$\frac{3}{16}$