Math assignments due in 5 hours

Read pages 321 and 322 where some crucial definitions are explained. EXAMPLE 1 on page 321 gives a few examples of various sample spaces.

1. Do YOUR TURN 1 on page 321.

In the box on page 323, your book lists SET OPERATIONS FOR EVENTS. Notice that these are the same as the set operations we used in Lesson 5.

The box on page 324 gives you the BASIC PROBABILITY PRINCIPLE. You may be asked to find multiple probabilities given the same sample set. Notice that the sample space (your denominator) will not change with every part of the problem, and therefore should be the first thing you find. If you look at parts a and b in EXAMPLE 6, you will see exactly this.

2. Read part c in EXAMPLE 6 on page 324. What can you conclude about P(something impossible)?

It is important to understand that probability always ranges between 0 and 1, with 0 being an impossible event and 1 being an event that is certain to happen. We also write 1 as 100% if we are talking in terms of percents. The yellow box on page 307 shows this.

You will need to be familiar with a standard deck of cards. The box in the middle of page 306 illustrates the various parts of a deck. Read through EXAMPLE 7 on page 325. Notice that as mentioned above, since each time you are drawing from a card from the full deck, your sample space doesn’t change and your denominator is always 52.

3. Do YOUR TURN 5 on page 325.

The top of page 331 shows you all of the different outcomes you could get if you tossed two dice together. You will not be given this chart on an exam, and so you should learn how to quickly replicate it.

4. How many different outcomes are there when tossing 2 dice?

5. Do YOUR TURN 1 on page 330.

6. Do YOUR TURN 2 on page 331.

The bottom of page 331 defines the complement rule. It explains that sometimes it is easier to find the complement and subtract it from 1 than it is to find the desired probability.

7. Explain in your own words why it would make sense for P(E) + P(E’) to equal 1.

Read through EXAMPLE 4 on page 332, which uses the complement rule.

8. Why is it easier to find P(sum is less than or equal to 3) and subtract it from 1 than it is to fine P(sum greater than 3)?

9. Do YOUR TURN 3 on page 332.

Often, a Venn diagram is useful in probability problems. Read through EXAMPLE 9 on page 335 and notice how by using the Venn diagram, part a and part b are easier to find.

10. Create a Venn Diagram based on the following information:

The probability that it will rain tomorrow is 39%, the probability that I will have an umbrella on me is 72% and the probability that it will rain tomorrow and I will have an umbrella on me is 27%.

a) Find the probability that it will rain tomorrow and I will not have an umbrella on me.

b) Find the probability that it will rain tomorrow or I will have an umbrella on me.