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

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


  1. A
    12
  2. B
    24
  3. C
    36
  4. D
    10 

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    Solution:

    From above data we have,
    Probability of red ball, P(R)=14 Probability of blue ball, P(B)=13 We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
    P(E)=Number of favourable outcomes n(E)Total possible outcomes n(S) The probability of an event always stays between 0 and 1, where zero represents impossible events and one indicates a sure event.
    The probability of orange ball is:
    P(Orange ball)=1-14+13
    P(Orange ball)=1-712
    P(Orange ball)=512
    Thus, the total number of balls is,
    P(Orange ball)=512=Number of orange ballsTotal number of balls
    512=10Total number of balls
    Total number of balls=10 × 125
    Total number of balls=24
    Thus, the total number of balls in the jar is 24.
    Hence, option 2 is correct.
     
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