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The probability of randomly selecting a red ball from a jar that contains only red, blue, and orange balls is one-quarter.
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The probability of selecting a blue ball from the same jar is one-third.
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If the jar contains 10 orange balls, find the total number of balls in the jar.
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There are only three possible outcomes for the color of the ball selected.
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They are red, blue, and orange.
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We know that the sum of all the probabilities of all possible outcomes is one.
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In this case, the probability of choosing a red ball plus the probability of choosing a blue ball plus the probability of choosing an orange ball is equal to one.
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We know that the probability of choosing a red ball is one-quarter and the probability of choosing a blue ball is one-third.
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So we can rewrite our equation as one-quarter plus one-third plus the probability of choosing an orange ball is equal to one.
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In order to be able to add one-quarter to one-third, we need to find the common denominator.
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The lowest common multiple of four and three is 12, so the lowest common denominator here is 12.
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To change one-quarter into twelfths, we multiply both the numerator and the denominator by three.
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That gives us three twelfths.
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Similarly, we multiply both the numerator and the denominator of one-third by four, and we get four twelfths.
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Three twelfths plus four twelfths is seven twelfths.
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So our equation becomes seven twelfths plus the probability of choosing an orange ball is equal to one.
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We can solve this equation to find the probability of choosing an orange ball by subtracting seven twelfths from both sides.
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We know that one whole is the same as twelve twelfths, so the probability of choosing an orange ball is twelve twelfths minus seven twelfths.
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The probability of choosing an orange ball is therefore five twelfths.
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Now at this point, it’s important to remember that all balls are equally likely to be chosen.
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This means that the probability of picking any ball is directly proportional to the number of balls of that color.
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There are 10 orange balls.
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If we call the total number of balls in the jar 𝑥, we can use this information to form an equation.
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Our equation is five twelfths of 𝑥 is equal to 10.
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We need to solve this equation for 𝑥.
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We’ll first multiply both sides by 12.
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That gives us five 𝑥 is equal to 120.
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Next, we’ll divide both sides by five.
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120 divided by five is 24, so 𝑥 is equal to 24.
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Since we said that the number of balls in the jar was equal to 𝑥, we can infer that there are 24 balls in the jar.