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.

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Answers ( No )

    0
    2021-11-15T19:36:48+00:00

    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:

    \displaystyle \frac{x}{25}

    And the probability of drawing a yellow ticket would be:

    \displaystyle \frac{25-x}{25}

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

    \displaystyle 0.50\cdot\frac{x}{25}+5.00\cdot\displaystyle \frac{25-x}{25}=3.20

    We solve it like this:

    Multiply both sides by 25 to clear of fractions:

    0.5x+5(25-x)=80

    Distribute:

    0.5x+125-5x=80

    Combine like terms:

    -4.5x+125=80

    Subtract 125 from both sides:

    -4.5x=-45

    Divide both sides by -4.5

    x=10

    There are 10 red tickets in the bag.

    0
    2021-11-15T19:37:01+00:00

    i would like one to. i came up with 6

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