Probability problem

[ucahdsu]

Please can someone help with the question? I think the answer is 2/3 but someone else thinks it's 1/3 - I need clarification please!

 

[Harry_the_cat]

Is the other side more likely to be black or white? This may help settle your argument.

 

[Romsek]

just apply Bayes

[MATH]P[B|A] = \dfrac{P[A|B]P[ B]}{P[A]}[/MATH]
[MATH]P[\text{card is black/black | black side is showing}] =\dfrac{P[\text{black side is showing|card is black/black}]P[\text{card is black/black}]}{P[\text{black side is showing}]} = \\ \dfrac{1 \cdot \frac 1 3}{\frac 1 3\left(\frac 1 2 + 1 + 0\right)} = \dfrac{\frac 1 3}{\frac 1 2} = \dfrac 2 3 [/MATH]

 

[Steven G]

Let the three cards be: B₁B₂, W₁W₂, BW

Let the 1st letter represent the color of the top of the card and the 2nd color represent the bottom color of the card.

The possibilities are B₁B₂, B₂B₁ and BW.

Does this help?