Suppose that we have a six-sided die with one face labeled with a 1, two faces l

Question

Suppose that we have a six-sided die with one face labeled with a 1, two faces labeled with a 2, and three faces labeled with a 3. Suppose also that Urn 1 has 4 black chips and 1 white chip, Urn 2 has 2 black chips and 2 white chips, and Urn 3 has 1 black chip and 4 white chips. You roll the die. If it comes up 1, you pick a chip from Urn 1. If it's 2, pick a chip from Urn 2. If it's 3, you pick a chip from Urn 3. If the chip that you end up picking is black, what is the probability that you rolled a 1?

Explanation / Answer

P( event of you rolling a 1 when the chip you picked up was black) = ?

We will use conditional probability formula.

P(get 1st urn) = 1/6

P(get 2nd urn) = 2/6

P(get 3rd urn) = 3/6

= P( get 1 urn)*P(get black in 1 urn)/ P( get 1 urn)*P(get black in 1 urn)+ P( get 2 urn)*P(get black in 2 urn) +P( get 3 urn)*P(get black in 3 urn)

= (1/6)(4/5) / ((1/6)(4/5) + (2/6)*(2/4) + (3/6)*(1/5))

=0.333

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