a number cube with faces numbered 1 to 6 is rolled 24 times. in theory, how many times would you expect to…

a number cube with faces numbered 1 to 6 is rolled 24 times. in theory, how many times would you expect to roll a number less than 5? a 16 b 20 c 2.5 d 12.5

a number cube with faces numbered 1 to 6 is rolled 24 times. in theory, how many times would you expect to roll a number less than 5? a 16 b 20 c 2.5 d 12.5

Answer

Explanation:

Step1: Calculate probability of rolling < 5

The numbers less than 5 on a 1 - 6 numbered cube are 1, 2, 3, 4. So there are 4 favorable outcomes out of 6 total outcomes. The probability $P$ of rolling a number less than 5 is $P=\frac{4}{6}=\frac{2}{3}$.

Step2: Calculate expected number of rolls

The cube is rolled 24 times. The expected number of times $E$ of rolling a number less than 5 is given by the formula $E = n\times P$, where $n = 24$ (number of trials) and $P=\frac{2}{3}$. So $E=24\times\frac{2}{3}=16$.

Answer:

A. 16