# Math 170

### due Tuesday, November 18

Remember that the homework needs to be handed in by 3 pm on Tuesday, November 18 and that no late homework will be accepted.

PROBLEMS:(each is worth 1 point.)
```The experiment for problems 1-5 consists of rolling a pair of dice (each die
has six faces numbered 1,2,3,4,5,6). Let E, F, G and H be the following events

E: the sum of the numbers thrown is 5;

F: the sum of the numbers thrown is 6;

G: the sum of the numbers thrown is even;

H: the sum of the numbers thrown is less than 6.

1) Find how many equally likely outcomes for this experiment; That is,
how many elements in the sample space.

2) Find how many elements in each of the events E, F, G and H.

3) Find the probability of each of the events E, F, G and H.

4) List the elements in the intersection of the events H and G and find
the probability of the intersection of the events H and G.

5) Find the probability of the union of the events G and H.

For the problems 6-10 the experiment consisting of rolling a fair die 6 times.

6) What is the probability of rolling 6 on the sixth trial?

7) What is the probability of rolling 6 on the sixth trial if we already
know that we rolled 6 on all the previous trials?

8) What is the probability of rolling 6 on the first and sixth trial and
rolling anything but 6 on all other trials?

9) What is the probability of rolling 6 exactly 4 times in all six trials?

10) What's the probability of rolling 6 at least 4 times in the first
five trials?

```