1. ## Probability Question

I'm stuck on this one question and I don't quite get it.

The probability that a teenager enjoys rock music in 0.7, and the probability that a teenager enjoys country music is 0.2. If only 1 in 10 teenagers enjoys rock as well as country, what is the probability that a teenager at random listens to either rock or country?

I don't quite understand where to break it up, where to put what numbers and what formula to use.

2. Originally Posted by risteek
I'm stuck on this one question and I don't quite get it.

The probability that a teenager enjoys rock music in 0.7, and the probability that a teenager enjoys country music is 0.2. If only 1 in 10 teenagers enjoys rock as well as country, what is the probability that a teenager at random listens to either rock or country?

I don't quite understand where to break it up, where to put what numbers and what formula to use.
Let $A$ be the event of a teen enjoying rock music, and let $B$ be the event of a teen enjoying country.

So we know that:

$P(A)=.7$
$P(B)=.2$
$P(A\cap B)=.1$

So it follows that we're after $P(A\cup B)$.

By definition, $P(A\cup B)=P(A)+P(B)-P(A\cap B)=.7+.2-.1=.8$

Does this make sense?

3. Yes it does. Thank you so much. I really need to work more at this but I'm getting better and this forum has been nothing but awesome. Thank you so much!