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)=0.409

Explanation:

Step1: Calculate 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 video game is not rated mature is $q=1 - p=1 - 0.136 = 0.864$.

Step2: Use the binomial probability formula for $k = 0$ successes in $n = 6$ trials

The binomial probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$. When $n = 6$, $k = 0$, $p = 0.136$, and $q = 0.864$, we have $C(6,0)=\frac{6!}{0!(6 - 0)!}=1$. Then $P(X = 0)=1\times(0.136)^{0}\times(0.864)^{6}$. Since any non - zero number to the power of 0 is 1, $P(X = 0)=(0.864)^{6}\approx0.409$.

Answer:

$0.409$