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The probability of selecting a red ball at random from a jar that contains only red, blue and orange ball is $14$ . The probability of selecting a blue ball at random from the same jar is $13$ . The probability of selecting a blue ball at random from the same jar is . If this jar contains 10 orange balls, then what is the total number of balls in the jar?

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answer is A.

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Detailed Solution

Given that there is a jar which contains red, blue and 10 orange balls.
And the probability of selecting a red ball is

14

.
The probability of selecting a blue ball is

13

.
Let the total number of balls in the jar as x.
Then the number of blue balls in a jar

= x 3

.
And the number of red balls

= x 4

.
And the number of orange balls

= 10

.
Sum up all the number of balls of all the colors and equate it to it by x,

x = x 4 + x 3 + 10 ⇒ 12 x = 3 x + 4 x + 120

⇒ 5 x = 120 ⇒ x = 24

There are a total of 24 balls in the jar.
Therefore, option 1 is correct.

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