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Question
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 = 10
5x = 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.
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