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.

The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is $\frac{1}{4}$. The probability of selecting a blue ball at random from the same jar is $\frac{1}{3}$. 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

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

Solution:

From above data we have,
Probability of red ball, $P\left(R\right)=\frac{1}{4}$ Probability of blue ball, $P\left(B\right)=\frac{1}{3}$ We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$ 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:
$P\left(\mathit{Orange ball}\right)=1-\left(\frac{1}{4}+\frac{1}{3}\right)$
$⇒P\left(\mathit{Orange ball}\right)=1-\frac{7}{12}$
$⇒P\left(\mathit{Orange ball}\right)=\frac{5}{12}$
Thus, the total number of balls is,
$⇒P\left(\mathit{Orange ball}\right)=\frac{5}{12}=\frac{\mathit{Number of orange balls}}{\mathit{Total number of balls}}$
$⇒\frac{5}{12}=\frac{10}{\mathit{Total number of balls}}$

$⇒\mathit{Total number of balls}=24$
Thus, the total number of balls in the jar is 24.
Hence, option 2 is correct.

Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)