# The Probability of Selecting a Red Ball at Random from a 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 1/3. - Mathematics

The probability of selecting a red ball at random from a 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 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

#### Solution

Here the jar contains red, blue and orange balls.
Let the number of red balls be x.
Let the number of blue balls be y.
Number of orange balls = 10
Total number of balls = x + y + 10
Now, let P be the probability of drawing a ball from the jar

P(a red ball) =x/(x+x+10)

1/4=x/(x+x+10)

4x=x+x+10

3x-y=10.........(i)

Next

P(a blueball) =y/(x+x+10)

1/3=y/(x+x+10)

3y=x+x+10

2y-x=10  ......(ii)

Multiplying eq. (i) by 2 and adding to eq. (ii), we get

6x - 2y = 20
-x + 2y = 105x      = 30

x=6

Subs. x = 6 in eq. (i), we get y = 8

Total number of balls = x + y + 10 = 6 + 8 + 10 = 24
Hence, total number of balls in the jar is 24.

Concept: Basic Ideas of Probability
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2014-2015 (March) All India Set 2
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