Total probability!

Level 1

There are $3$ bags -

Bag $1$ ▶ 2 white balls and 3 red balls.

Bag $2$ ▶ 4 white balls and 5 red balls.

Bag $3$ ▶ 2 white balls and 2 red balls.

A bag is selected at random and a ball is drawn from it, what is the probability that the ball is white?

\frac{119}{270}

\frac{149}{270}

\frac{127}{270}

\frac{121}{270}

1 solution

Jordan Cahn
Oct 11, 2018

$\begin{aligned} \overbrace{\frac{1}{3}\times\frac{2}{5}}^{\text{Prob. of drawing white from Bag }1} + \underbrace{\frac{1}{3}\times\frac{4}{9}}_{\text{Prob. of drawing white from Bag }2} + \overbrace{\frac{1}{3}\times\frac{2}{4}}^{\text{Prob. of drawing white from Bag }3} &= \frac{2}{15} + \frac{4}{27} + \frac{1}{6} \\ &= \frac{36}{270} + \frac{40}{270} + \frac{45}{270} \\ & = \boxed{\frac{121}{270}} \end{aligned}$

Total probability!

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