Probability

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag......Can someone help me in basics of probability...????

Assuming the balls are indistinguishable to the person drawing them,
also assuming we are calculating the probability on the first draw,
then in order for the probability of drawing a blue ball being
twice the probability of drawing a red ball initially,
there must be twice as many blue balls in the bag.

Hello, "Nelson01!

chrisr is absolutely correct . . . and has the best solution!

I'll do it the Long Way . . .

A bag contains 5 red balls and some blue balls.
If the probability of drawing a blue ball is double that of a red ball,
find the number of blue balls in the bag.

Click to expand...

\(\displaystyle \text{The bag contains: }\:\begin{Bmatrix} \text{5 red balls} \\ b\text{ blue balls} \end{Bmatrix}\)

There is a total of \(\displaystyle b+5\) balls.


. . \(\displaystyle \begin{array}{ccc}P(\text{blue}) &=& \dfrac{b}{b+5} \\ \\[-3mm] P(\text{red}) &=& \dfrac{5}{b+5} \end{array}\)


\(\displaystyle P(\text{blue}) \;=\; 2\times P(\text{red}) \quad\Rightarrow\quad \frac{b}{b+5} \;=\;2\cdot\frac{5}{b+5}\)


\(\displaystyle \text{Therefore: }\;\frac{b}{b+5} \:=\:\frac{10}{b+5} \quad\Rightarrow\quad\boxed{ b\,=\,10}\)

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