Video: CBSE Class X • Pack 4 • 2015 • Question 15

CBSE Class X • Pack 4 • 2015 • Question 15

02:54

Video Transcript

The probability of randomly selecting a red ball from a jar that contains only red, blue, and orange balls is one-quarter. The probability of selecting a blue ball from the same jar is one-third. If the jar contains 10 orange balls, find the total number of balls in the jar.

There are only three possible outcomes for the color of the ball selected. They are red, blue, and orange. We know that the sum of all the probabilities of all possible outcomes is one. 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.

We know that the probability of choosing a red ball is one-quarter and the probability of choosing a blue ball is one-third. So we can rewrite our equation as one-quarter plus one-third plus the probability of choosing an orange ball is equal to one.

In order to be able to add one-quarter to one-third, we need to find the common denominator. The lowest common multiple of four and three is 12, so the lowest common denominator here is 12. To change one-quarter into twelfths, we multiply both the numerator and the denominator by three. That gives us three twelfths. Similarly, we multiply both the numerator and the denominator of one-third by four, and we get four twelfths. Three twelfths plus four twelfths is seven twelfths. So our equation becomes seven twelfths plus the probability of choosing an orange ball is equal to one.

We can solve this equation to find the probability of choosing an orange ball by subtracting seven twelfths from both sides. 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. The probability of choosing an orange ball is therefore five twelfths.

Now at this point, it’s important to remember that all balls are equally likely to be chosen. This means that the probability of picking any ball is directly proportional to the number of balls of that color. There are 10 orange balls. If we call the total number of balls in the jar 𝑥, we can use this information to form an equation.

Our equation is five twelfths of 𝑥 is equal to 10. We need to solve this equation for 𝑥. We’ll first multiply both sides by 12. That gives us five 𝑥 is equal to 120. Next, we’ll divide both sides by five. 120 divided by five is 24, so 𝑥 is equal to 24. 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.

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