Question

video game video games are rated according to the content. the average age of a gamer is 33 years old. in a recent year, 16.4% of the video games were rated mature. choose 4 purchased games at random. find the following probabilities. round the final answers to three decimal places. part: 0 / 2 part 1 of 2 (a) find the probability that none of the four were rated mature. p(none were rated mature)=

Explanation:

Step1: Determine the probability of a non - mature game

The probability that a video game is rated mature is $p = 0.164$. So the probability that a video game is not rated mature is $q=1 - p=1 - 0.164 = 0.836$.

Step2: Use the binomial probability formula for $k = 0$

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, and $q$ is the probability of failure on a single trial. Here, $n = 4$, $k = 0$, $p = 0.164$, and $q = 0.836$. Since $C(n,0)=1$ for any non - negative integer $n$, we have $P(X = 0)=C(4,0)\times(0.164)^{0}\times(0.836)^{4}$.
Since $(0.164)^{0}=1$ and $C(4,0) = 1$, then $P(X = 0)=(0.836)^{4}$.

Step3: Calculate the result

$(0.836)^{4}=0.836\times0.836\times0.836\times0.836\approx0.489$.

Answer:

$0.489$