# The Probability of Selecting a Red Ball at Random from the Jar that Contains Only Red, Blue and Orange Balls is 1 4 . the Probability of Selecting a Blue Ball at Random from the Same Jar - Mathematics

Short Note
Sum

The probability of selecting a red ball at random from the jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

#### Solution

It is given that,

P(getting a red ball) =1/4  and P(getting a blue ball) =1/3

Let P(getting an orange ball) be x.

Since, there are only 3 types of balls in the jar, the sum of probabilities of all the three balls must be 1.

therefore  1/4 + 1/3 + x = 1

rArr x = 1 - 1/4 -1/3

rArr x = (12-3-4)/12

rArr x = 5/12

∴ P(getting an orange ball) =5/12

Let the total number of balls in the jar be n.

∴ P(getting an orange ball) = 10/n

rArr 10/n = 5/12

rArr n = 24

Thus, the total number of balls in the jar is 24.

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 15 Probability
Exercise 15B | Q 10 | Page 697