# Thread: Probability of rolling two dice

1. ## Probability of rolling two dice

Link: http://i43.tinypic.com/mu7dzn.jpg

This is the most confusing chapter out of all the chapters. I really appreciate it if you can help me through these problems. Thank you so much.

2. Originally Posted by krzyrice Link: http://i43.tinypic.com/mu7dzn.jpg

This is the most confusing chapter out of all the chapters. I really appreciate it if you can help me through these problems. Thank you so much.
I've put my answers in spoiler tags, I hope you'll try to work them out for yourself

1. This means the chance of A happening. In this case rolling a 1, 2 or 3 of a 6 sided die.

Spoiler:

$\displaystyle P(A) = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

2. This is the chance of A or B happening and is equal to
P(A U B) = P(A) + P(B) - P(A)P(B)

Spoiler:
$\displaystyle \frac{1}{2} + \frac{2}{3} - \frac{1 \times 2}{2 \times 3} = \frac{5}{6}$

3. P(A n B) = P(A)P(B) and it's the chance of both happening

Spoiler:
$\displaystyle \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$

4. This means the chance of b not happening and so it is equal to 1-P(B)

Spoiler:
$\displaystyle 1-\frac{2}{3} = \frac{1}{3}$

5. This one means the chance of a happening and b not happening:

Spoiler:

$\displaystyle \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

3. Thank you so much for the help! The spoiler technique was very useful in helping me check and to learn from my mistakes. Overall it wasn't as bad as I thought. You are a very good teacher thank you so much for help me with this.

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