Question

video game video games are rated according to the content. the average age of a gamer is 34 years old. in a recent year, 13.6% of the video games were rated mature. choose 6 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 six were rated mature. p(none were rated mature) =

Explanation:

Step1: Determine the probability of a single - game not being rated mature

The probability that a video game is rated mature is $p = 0.136$. So the probability that a single video game is not rated mature is $q=1 - p=1 - 0.136 = 0.864$.

Step2: Use the binomial probability formula for $n = 6$ and $k = 0$

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, $n = 6$, $k = 0$, $p = 0.136$, and $q = 0.864$. Also, $C(n,k)=\frac{n!}{k!(n - k)!}$, and when $k = 0$, $C(6,0)=\frac{6!}{0!(6 - 0)!}=1$. Then $P(X = 0)=C(6,0)\times(0.136)^{0}\times(0.864)^{6 - 0}$. Since any non - zero number to the power of 0 is 1, $(0.136)^{0}=1$. So $P(X = 0)=1\times1\times(0.864)^{6}$.

Step3: Calculate the result

$(0.864)^{6}=0.864\times0.864\times0.864\times0.864\times0.864\times0.864\approx0.406$.

Answer:

$0.406$