a number cube with faces numbered 1 to 6 is rolled 12 times. in theory, how many times would you expect to…

a number cube with faces numbered 1 to 6 is rolled 12 times. in theory, how many times would you expect to roll a number less than 4? a 2 b 6 c 8 d 10
Answer
Answer:
B. 6
Explanation:
Step1: Calculate probability of rolling < 4
The numbers less than 4 on a 1 - 6 numbered cube are 1, 2, 3. So there are 3 favorable outcomes out of 6 total outcomes. The probability $P=\frac{3}{6}=\frac{1}{2}$.
Step2: Calculate expected number of rolls
The cube is rolled 12 times. The expected number of times to roll a number less than 4 is $n = P\times N$, where $N = 12$ and $P=\frac{1}{2}$. So $n=\frac{1}{2}\times12 = 6$.