## A bag contains 25 tickets, each colored either red or yellow. Red tickets are worth $0.50, and yellow tickets are worth $5.00. If the expect

Question

A bag contains 25 tickets, each colored either red or yellow. Red tickets are worth $0.50, and yellow tickets are worth $5.00. If the expected value of a ticket drawn at random from this bag is $3.20, how many of the tickets are red?

The answer to the question is 10, I just need an explanation why.

## Answers ( No )

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:

And the probability of drawing a yellow ticket would be:

Then we multiply each probability by their values and sum up to get the expected value, so that we get the equation:

We solve it like this:

Multiply both sides by 25 to clear of fractions:

Distribute:

Combine like terms:

Subtract 125 from both sides:

Divide both sides by -4.5

There are 10 red tickets in the bag.

i would like one to. i came up with 6