MTH 216
Checkpoint 4
A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-
course meal? Use the multiplication principle with two groups of items.
There are 70 ways a person can order a two-course meal. (Multiply 10 times 7)
Pizza House offers 3 different salads, 3 different kinds of pizza, and 3 different desserts. How many
different three course meals can be ordered?
How many different meals can be ordered? 27 (Multiply 3 * 3 * 3 to get answer)
A restaurant offers 4 appetizers and 7 main courses. In how many ways can a person order a two-
course meal? Use the multiplication principle with two groups of items.
There are 28 way a person can order a two-course meal
Pizza House offers 2 different salads, 4 different kinds of pizza, and 4 different desserts. How many
different three course meals can be ordered?
How many different meals can be ordered? 32
Suppose we describe the weather as either sunny (S) or frigid (F). Answer parts (a) and (b) below.
Using the letters S and F, list all the possible outcomes for the weather on two consecutive days.
SS, SF, FS, FF
If we are only interested in the number of S days, what are the possible events for two consecutive
days.
0, 1, 2
Suppose we describe the weather as either clear (C) or frigid (F).
Answer parts (a) and (b) below. Using the letters C and F, list all the possible outcomes for the weather on
two consecutive days.
CC, FC, CC, FF
If we are only interested in the number of C days, what are the possible events for two consecutive
days.
0, 1, 2
Use the theoretical method to determine the probability of the following outcome and event. State
any assumptions made. Tossing two coins and getting either one head or two heads
Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 3/4
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a black card?
, ½
You toss a coin 300 times and get 243 heads. Complete parts (a) - (c) below.
Determine the relative frequency probability.
243/300 or 0.81
Determine the expected frequency of the event.
150/300 or 0.50
Do you have reason to suspect the coin is unfair? Explain
Yes, because the relative frequency is not near the expected frequency.
Use the theoretical method to determine the probability of the following event. Sharing a birthday
with another person when you both have birthdays in December
1/31
You toss a coin 200 times and get 26 heads. Complete parts (a)-(c) below.
Determine the relative frequency probability.
26/200 or 0.13
Determine the expected frequency of the event.
100/200 or 0.50
Do you have reason to suspect the coin is unfair? Explain
Yes, because the relative frequency is not near the expected frequency.
Use the theoretical method to determine the probability of the following event. Sharing a birthday
with another person when you both have birthdays in February (not born on a leap year).
1/28
Find the odds for and the odds against the event rolling a fair die and getting a 4, a 2, or a 6.
The odds for the event are 1 to 1.
The odds against the event are 1 to 1
Find the odds for and the odds against the event rolling a fair die and getting a 6 or a 3.
The odds for the event are 1 to 2
The odds against the event are 2 to 1
The odds on (against) your bet are 3 to 4. If you bet $8 and win, how much will you gain?
$6 – Divide the bet by the “to” amount; then multiply that number the odd amount (3).
Find the odds for and the odds against the event rolling a fair die and getting a 2 or a 5.
The odds for the event are 1 to 2
The odds against the event are 2 to 1
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a red 9?
, 2/52 or 1/26
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a red king?
2/52 or 1/26
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black 2 or jack of diamonds from a standard deck of
cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a red 10 or a queen of diamonds from a standard deck
of cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Randomly meeting someone whose Social Security number ends in
the same digit as yours.
Using the theoretical method, the probability is 1/10
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a black face card?
6/52 or 3/26
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black queen or ace of clubs from a standard deck of
cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black 10 or ace of hearts from a standard deck of cards.
The theoretical method should be used.
The probability of drawing a black 10 or ace of hearts is 3/52
Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why
not? What does the law of large numbers tell you about the results you are likely to get?
You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many
heads will occur.
What does the law of large numbers tell you about the results you are likely to get?
The proportion of heads should approach 0.5 as the number of tosses increases.
Checkpoint 4
A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-
course meal? Use the multiplication principle with two groups of items.
There are 70 ways a person can order a two-course meal. (Multiply 10 times 7)
Pizza House offers 3 different salads, 3 different kinds of pizza, and 3 different desserts. How many
different three course meals can be ordered?
How many different meals can be ordered? 27 (Multiply 3 * 3 * 3 to get answer)
A restaurant offers 4 appetizers and 7 main courses. In how many ways can a person order a two-
course meal? Use the multiplication principle with two groups of items.
There are 28 way a person can order a two-course meal
Pizza House offers 2 different salads, 4 different kinds of pizza, and 4 different desserts. How many
different three course meals can be ordered?
How many different meals can be ordered? 32
Suppose we describe the weather as either sunny (S) or frigid (F). Answer parts (a) and (b) below.
Using the letters S and F, list all the possible outcomes for the weather on two consecutive days.
SS, SF, FS, FF
If we are only interested in the number of S days, what are the possible events for two consecutive
days.
0, 1, 2
Suppose we describe the weather as either clear (C) or frigid (F).
Answer parts (a) and (b) below. Using the letters C and F, list all the possible outcomes for the weather on
two consecutive days.
CC, FC, CC, FF
If we are only interested in the number of C days, what are the possible events for two consecutive
days.
0, 1, 2
Use the theoretical method to determine the probability of the following outcome and event. State
any assumptions made. Tossing two coins and getting either one head or two heads
Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 3/4
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a black card?
, ½
You toss a coin 300 times and get 243 heads. Complete parts (a) - (c) below.
Determine the relative frequency probability.
243/300 or 0.81
Determine the expected frequency of the event.
150/300 or 0.50
Do you have reason to suspect the coin is unfair? Explain
Yes, because the relative frequency is not near the expected frequency.
Use the theoretical method to determine the probability of the following event. Sharing a birthday
with another person when you both have birthdays in December
1/31
You toss a coin 200 times and get 26 heads. Complete parts (a)-(c) below.
Determine the relative frequency probability.
26/200 or 0.13
Determine the expected frequency of the event.
100/200 or 0.50
Do you have reason to suspect the coin is unfair? Explain
Yes, because the relative frequency is not near the expected frequency.
Use the theoretical method to determine the probability of the following event. Sharing a birthday
with another person when you both have birthdays in February (not born on a leap year).
1/28
Find the odds for and the odds against the event rolling a fair die and getting a 4, a 2, or a 6.
The odds for the event are 1 to 1.
The odds against the event are 1 to 1
Find the odds for and the odds against the event rolling a fair die and getting a 6 or a 3.
The odds for the event are 1 to 2
The odds against the event are 2 to 1
The odds on (against) your bet are 3 to 4. If you bet $8 and win, how much will you gain?
$6 – Divide the bet by the “to” amount; then multiply that number the odd amount (3).
Find the odds for and the odds against the event rolling a fair die and getting a 2 or a 5.
The odds for the event are 1 to 2
The odds against the event are 2 to 1
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a red 9?
, 2/52 or 1/26
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a red king?
2/52 or 1/26
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black 2 or jack of diamonds from a standard deck of
cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a red 10 or a queen of diamonds from a standard deck
of cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Randomly meeting someone whose Social Security number ends in
the same digit as yours.
Using the theoretical method, the probability is 1/10
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of
drawing a black face card?
6/52 or 3/26
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black queen or ace of clubs from a standard deck of
cards.
The theoretical method should be used.
3/52
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or
estimate the following probability. Drawing a black 10 or ace of hearts from a standard deck of cards.
The theoretical method should be used.
The probability of drawing a black 10 or ace of hearts is 3/52
Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why
not? What does the law of large numbers tell you about the results you are likely to get?
You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many
heads will occur.
What does the law of large numbers tell you about the results you are likely to get?
The proportion of heads should approach 0.5 as the number of tosses increases.
