Question

A bag contains 10 white balls and X black balls. If the probability of drawing white balls is double that black ball then answer the following: Find the value of X.
A. 5
B. 10
C. 20
D. 15

Answer 1

Hint: We have given the number of white balls and the number of black balls from that we can find the probability of both color balls using the formula \[\dfrac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\]
and let the probability of white balls be P(W) and probability of black balls be P(B) and to find X, use the equation \[P(W)=2\times P(B)\].

Complete step by step solution:
 In the above question, we are given that,
The number of white balls in the bag = 10
And the number of black balls in the bag = X
So the total number of balls in the bag = 10+X
And we know that the probability of an event occurred is given by the formula as shown below
= \[\dfrac{\text{number of favorable outcomes}}{\text{total number of outcomes}}\]
Total number of outcomes = 10+X
So the probability of drawing a white ball from the bag is
\[P(W)=\dfrac{10}{10+X}..........\left( 1 \right)\]
And the probability of drawing a black ball from the bag is
\[P(B)=\dfrac{X}{10+X}............\left( 2 \right)\]
Now we are given that the probability of drawing white balls is double that black balls
So we can say that
Probability of drawing white ball = 2 \[\times \] probability of black ball
\[P(W)=2\times P(B)\]
\[\dfrac{10}{10+X}=2\times \dfrac{X}{10+X}...........\left( 3 \right)\]
Which we can write as
\[10=2X\]
\[\begin{align}
  & \Rightarrow X=5 \\
 & \\
\end{align}\]
So for the probability of white balls being double that black balls, the number of black balls in the bag must be 5.
Hence the correct answer is option (A).

Note: The possibility for the mistake is that students may get confused while understanding the question. They can elaborate it as 2 \[\times \] P(W) = P(B). Some students try to find the answer from options. They might think that if there are 10 white balls, and the probability of drawing white ball is double that of black ball, then the number of black balls would be \[\dfrac{10}{2}=5\] .
This might not always be correct and is not the right method to solve the question. So, this must not be adopted.