Name _____________________________ Class Period__________ Date_________________

POW 2: ProbabilityDue September 22nd (Monday) or September 23rd (Tuesday)

The acronym P.O.W. stands for Problems of the Week. This series of homework problems will be a combination of different mathematical concepts that you have already explored in grade school or which we will explore this year. You will be given a POW once each week and it will be collected the following week. We will discuss hints for the POW during the week. When completing your POW please be sure to:

Read the directions carefully and answer the given question(s). Show all work for complete credit and circle your final solution. Staple this sheet to the top of your work if there are multiple pages to turn in. READ your POW the day you receive it. If you have questions about the assignment, you should be

prepared to ask them during your Wednesday Colloquium Math class.

PART ONE Determining Outcomes and Probability: Complete all questions on a separate sheet of paper, including the table for 18 a. For 18 b, c and d provide your answer using complete sentences and explain your reasoning.

PART ONE (cont.)

Before answering question 19 below, find the probability distribution table you created for the sum of two standard six-sided dice. If you cannot find your table, recreate it before answering the new problem below.

PART TWO – Calculating Outcomes and Probability

Solve the problems below using your knowledge of probability. Show your thinking to receive credit.

1. Patrick tosses four dimes in the air. What is the probability that all four dimes will land on tails?

2. Armani tosses rolls two dice. What is the probability that the two dice show different numbers?

3. Jordan rolls two dice. What is the probability that a seven DOES NOT come up?

4. The sample space for the set of the 11 possible sums for two dice are: {2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 }. Since two of these 11 possibilities correspond to a sum of 9 or 10, some people might be tempted to say

the probability of a sum of 9 or 10 is 211. Explain why this reasoning is incorrect.

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5. In a family with three children, what is the probability that, all three children are girls? (Assume that having a girl and having a boy are equally likely.)

What is the P(two girls) in a family of three children?

6. “OR” EXAMPLES:

a. If a card is drawn from our set of overhead cards (red, green or blue numbered 1 - 5), find the probability that the card drawn is red or blue.

b. If a card is drawn from a standard deck of 52 cards, find the probability that the card is an ace or a diamond.

c. If two dice are rolled, find the probability that the sum is 6 or doubles are rolled.

d. If two dice are rolled, find the probability that the sum is 3 or the sum is 9.

7. “AND” EXAMPLES:

a. What is the probability of drawing a card that is red and even from a standard deck of 52 cards?

b. What is the probability of drawing a card that is black and less than 5 from a standard deck of 52 cards?

c. What is the probability of rolling three 6's in three rolls of a die?

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PART THREE – Calculating Probability from a Table

Use the table below, which gives the areas of concentration of 400 students at a small college.

Area of Concentration

ClassFreshman Sophomore Junior Senior Totals

Natural Sciences

50 35 33 29 147

Social Sciences 20 25 28 24 97

Humanities 40 40 39 37 156

Totals 110 100 100 90 400

1. If a student is selected at random, what is the probability that:

A. The student’s area of concentration is the natural sciences?

B. The student is a freshman in the social sciences?

2. What is the probability that:

C. A senior’s area of concentration is the natural sciences?

D. A student in the natural sciences is a senior?

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