Three balls

Probability Level pending

There are three balls in a bag, two blue and one red.

You pick one out at random.

Then your friend picks one out and reveals that he picked a blue ball.

What is the probability that you picked a blue ball?

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0

\frac{3}{4}

1

\frac{1}{4}

\frac{2}{3}

\frac{1}{2}

None of these answers

\frac{1}{3}

1 solution

Geoff Pilling
Dec 7, 2016

Call the two blue balls, $B_1$ and $B_2$ .

There are six possible scenarios for picking three balls:

You	Friend
$B_1$	$B_2$
$B_1$	$R$
$B_2$	$B_1$
$B_2$	$R$
$R$	$B_1$
$R$	$B_2$

We can eliminate the second and fourth possibilities since we know your friend picked a blue ball. Of the remaining possibilities, in two of them you picked a red ball and in two of them you picked a blue ball.

So, the probability you picked a blue ball is $\boxed{\frac{1}{2}}$

Three balls

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1 solution

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