Question

a dice is rolled 4 times. what is the probability of showing a 3 on every roll? (round to 4 decimal places)

Explanation:

Step1: Probability of getting 3 on one roll

A standard die has 6 faces. The probability of getting a 3 on a single roll is $\frac{1}{6}$.

Step2: Probability of independent events

Since the rolls are independent events, the probability of getting a 3 on 4 consecutive rolls is the product of the probabilities of getting a 3 on each individual roll. So the probability $P = (\frac{1}{6})^4$.

Step3: Calculate the value

$(\frac{1}{6})^4=\frac{1}{1296}\approx0.0008$

Answer:

0.0008