Question

The popularity of computer, video, online, and virtual reality games has raised concerns about their ability to negatively impact youth. The data in this exercise are based on a recent survey of 14 ‑ to 18 ‑year‑olds in Connecticut high schools. Assume the table displays the grade distributions of boys who have and have not played video games.

Grade Average
A's and B's C's D's and F's
Played games 730 444 190
Never played games 214 137 87
Give the conditional distribution of the grades of those who have played games. (Enter your answers rounded to two decimal places.)

Answer 1

P(The grade of the boy is A| He has played video games)

is,
`\simeq 0.54`

P(The grade of the boy is B| He has played video games)

is
`\simeq 0.33`

P(The grade of the boy is C| He has played video games)

is
`\simeq 0.14`

Explanation:

The total no. of boys who have played video games,

= (730 + 444 + 190)

=1360

Now, from the given data,

P(The grade of the boy is A| He has played video games)

=
`\frac {730}{1360}`

`\simeq 0.54`

P(The grade of the boy is B| He has played video games)

=
`\frac {444}{1360}`

`\simeq 0.33`

P(The grade of the boy is C| He has played video games)

=
`\frac {190}{1360}`

`\simeq 0.14`