9 a die is rolled 4 times. what is the chance that none of the rolls show 4 or more spots?\na. less than…

Explanation:

Step1: Calculate single - roll probability

A standard die has 6 faces. The numbers less than 4 are 1, 2, 3. So the probability of getting a number less than 4 in a single roll is $p=\frac{3}{6}=\frac{1}{2}$.

Step2: Use independent - event formula

Since the rolls of the die are independent events, the probability of getting a number less than 4 in all 4 rolls is $P = (\frac{1}{2})\times(\frac{1}{2})\times(\frac{1}{2})\times(\frac{1}{2})=\left(\frac{1}{2}\right)^4$.

Step3: Calculate the final probability

$\left(\frac{1}{2}\right)^4=\frac{1}{16}= 0.0625 = 6.25%$.

Answer:

C. 6.25%