Answer:
10 red tickets
Step-by-step explanation:
Let us call x the number of red tickets.
Notice since there are 25 tickets in the bag then we have 25-x yellow tickets.
Now, the probability of drawing a red ticket would be:
[tex]\displaystyle \frac{x}{25}[/tex]
And the probability of drawing a yellow ticket would be:
[tex]\displaystyle \frac{25-x}{25}[/tex]
Then we multiply each probability by their values and sum up to get the expected value, so that we get the equation:
[tex]\displaystyle 0.50\cdot\frac{x}{25}+5.00\cdot\displaystyle \frac{25-x}{25}=3.20[/tex]
We solve it like this:
Multiply both sides by 25 to clear of fractions:
[tex]0.5x+5(25-x)=80[/tex]
Distribute:
[tex]0.5x+125-5x=80[/tex]
Combine like terms:
[tex]-4.5x+125=80[/tex]
Subtract 125 from both sides:
[tex]-4.5x=-45[/tex]
Divide both sides by -4.5
[tex]x=10[/tex]
There are 10 red tickets in the bag.
