	Watch Violent Movie	Watch Nonviolent Movie
Remember brand name	$.15$	$.18$
Do not remember brand name	$.35$	$.32$

	Watch Violent Movie	Watch Nonviolent Movie
Remember brand name	$.15$	$.18$
Do not remember brand name	$.35$	$.32$

Many critics of television claim that there is too much violence and that it has a negative effect on society. There may also be a negative effect on advertisers. To examine this issue, researchers developed two versions of a cops-and-robbers made-for-television movie. One version depicted several violent crimes, and the other removed these scenes. In the middle of the movie, one 60-second commercial was shown advertising a new product and brand name. At the end of the movie, viewers were asked to name the brand. After observing the results, the researchers produced the following table of joint probabilities. What proportion of viewers remember the brand name?

Watch Violent Movie Watch Nonviolent Movie

Remember brand name $.15$ $.18$

Do not remember brand name $.35$ $.32$

	Watch Violent Movie	Watch Nonviolent Movie
Remember brand name	$.15$	$.18$
Do not remember brand name	$.35$	$.32$

Solution

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Answered 1 year ago

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Define the events as follows:

$A_1$ - Viewers watch a violent movie.
$A_2$ - Viewers watch a non-violent movie.
$B_1$ - Viewers remember the brand name.
$B_2$ - Viewers do not remember the brand name.

From the given table of joint probabilities, we have:

\begin{align*} P(A_1 \,\text{and}\,B_1)&=0.15\\ P(A_2 \,\text{and}\,B_1)&=0.18 \end{align*}

\begin{align*} P(A_1 \,\text{and}\,B_2)&=0.35\\ P(A_2 \,\text{and}\,B_2)&=0.32 \end{align*}

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