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Problems 1-4

**Please give your answers as decimals rounded to TWO decimal places (round to the hundredths place).**

**Canvas may add additional zeros to the end of your answer. For example, if you input 0.25, Canvas may correct it to 0.2500 automatically. We will grade this as 0.25. Please disregard this Canvas glitch.**

**Hint: These are simple probability problems using the basic formula for probability.**

An urn contains 4 blue balls, 6 red balls, and 3 green balls and 6 yellow balls. You stick your hand in and pull out a ball without looking.

What is the probability of the following outcomes?

**Question 1**** .**

What is the probability of selecting a red ball?

**Question 2**** .**

What is the probability of selecting a blue ball?

**Question 3****.**

What is the probability of selecting a yellow ball or a green ball?

**Question 4**** .**

Assume you chose a red ball. Do NOT put it back into the urn. You then pick another ball from the urn. Find the probability it will be another red ball.

Problems 5-6: Dice

These two questions involve one die.

**Please give your answers as decimals rounded to TWO decimal places (round to the hundredths place).**

**Question 5****4 .**

What is the probability of obtaining a 3 or a 5 on ONE roll of a single die?

**Question 6****4 .**

What is the probability of obtaining an odd number on one roll of a die?

Problems 7-13: Dice continued

For these problems, you must draw a dice table, and answer questions relating to two dice.

**Please give your answers as decimals rounded to TWO decimal places (round to the hundredths place).**

**Question 7****5 .**

Draw a dice table on the PDF document noted in the directions. This must be drawn in your own handwriting.

Upload your drawing.

Now that you have drawn the dice table, find the probability. These problems use some abbreviations: P(4, 2 dice) means what is the probability of getting a 4 when you roll two dice.

**Please give your answers as decimals rounded to TWO decimal places (round to the hundredths place).**

**Question 8**** .**

If you roll a **PAIR** of dice, what is P(7, 2 dice)?

**Question 9**** .**

If you roll a **PAIR** of dice, what is P(3, 2 dice)?

**Question 10**** .**

If you roll a **PAIR** of dice, what is P(10, 2 dice)?

**Question 11**** .**

If you roll a **PAIR** of dice, what is P(5, 2 dice)?

**Question 12**** .**

If you roll a **PAIR** of dice, what is P(<6, 2 dice)?

**Question 13**** .**

If you roll a **PAIR** of dice, what is P(>5, 2 dice)?

Problems 14-18: Coins

Draw Pascal’s Triangle and calculate the probability of the following coin flip problems.

**Please give your answers as decimals rounded to TWO decimal places (round to the hundredths place).**

**Question 14**** .**

Draw Pascal’s Triangle on the PDF document noted in the directions. This must be drawn in your own handwriting. Upload your drawing.

Upload

Choose a File

**Question 15**** .**

If you flip five coins what is the probability that you will get two heads? (that means exactly two heads.)

**Question 16**** .**

If you flip five coins what is the probability that you will get three tails?

**Question 17**** .**

If you flip five coins what is the probability that you will get at least three heads?

**Question 18****.**

If you flip five coins what is the probability that you will get fewer than two tails?

Problems 19-22: Lottery

In class, we looked at the probability of winning a lottery such as Megabucks. To play, one has to pick six numbers between **1 and 48**, with no repeated numbers. The chance of your number being the winning number is

112271512 or 0.0000000815

When the lottery first came out in Massachusetts, you only had to pick six different numbers between 1 and 36. Use this information to answer questions 19-23.

If you bought one ticket for this type of lottery:

**Question 19****.**

Calculate the total possible combinations of six numbers between 1 and 36, ** including** different orderings of the same numbers. This answer must be written in standard form. Scientific notation will not be accepted.

NOTE: Canvas removes any commas you enter for large numbers!

**Question 20**** .**

Calculate the number of ways each of these combinations of 6 numbers could be arranged.

**Question 21**** .**

Calculate the total possible of outcomes ** excluding** different orderings of the same numbers.

NOTE: Canvas removes any commas you enter for large numbers!

**Question 22**** .**

Find the probability of winning the lottery as a fraction and as a decimal. ** Do NOT** round – just write down all the numbers you see on the screen of your calculator.

Problems 23-28

Calculate the following. You may use the factorial key on your calculator. Some of these are a bit tricky – you may need to do some simplifying before using your calculator.

NOTE: Canvas removes any commas you enter for large numbers!

**Question 23**** .**

7!

**Question 24**

15!

**Question 25****.**

15!/6! fraction

**Question 26****.**

25! / (25−10)! fraction

**Question 27**

48! / 6!×42! fraction

**Question 28****.**

0!