# Thread: Probability of rolling two dice

1. ## Probability of rolling two dice

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

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.