# Math 170

### homework 5

### 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.

**
READINGS:** Sections 4.1-13.

**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?