Question

1. Marcus randomly draws tokens from a bag containing 10 blue tokens, 8 green tokens, and 12 red tokens. The first draw is a green token. How many total outcomes were possible for this event?
A.8
B.10
C.22
D.30

2. Marcus randomly draws tokens from a bag containing 10 blue tokens, 8 green tokens, and 12 red tokens. The first draw is a green token. How many favorable outcomes are possible for this event?
A.8
B.10
C.22
D.30

3. There are 5 red socks, 2 white socks, and 3 blue socks in a basket. What is the probability of picking a pair of red socks?
A.2/9
B.7/90
C.1/5
D.9/100

4. A coin is flipped 50 times and lands on heads 32 times. What is the experimental probability the coin will land on heads on the next flip?
A.32%
B.50%
C.56%
D.64%

5. The probability of an event is 3/10. What are the odds of the same event?
A.10/13
B.3/13
C.7/10
D.3/7

6. In a 10 person race, how many different outcomes are there for first, second, and third place?
A.1,000
B.720
C.120
D.30

7. A coin is flipped 50 times and lands on heads 28 times. What is the theoretical probability that the coin will land on heads on the next flip?
A.32%
B.50%
C.56%
D.64%

8. A special at a local restaurant allows customers to choose one entrée and one dessert for $5.99. There are 8 entrées and 5 desserts to choose from. Use the Fundamental Counting Principle to calculate the total number of specials available.
A.8
B.13
C.26
D.40

9. There are 30 red soda cans and 20 green soda cans in an ice chest. What are the odds of reaching in and grabbing a green can?
A.3/2
B.2/3
C.3/5
D.2/5

10. A coin is flipped, then a 6-sided die is rolled. What is the probability of getting heads and an even number?
A.1/2
B.1/4
C.1/6
D.1/12

11. Using the letters in the word INNOVATIVE, find the number of permutations that can be formed using 4 letters at a time. Show your work or explain how you got your answer.

12. The gym has 11 different types of machines in the weight room. Geoff has time to use only 3 of them this afternoon. How many different combinations of machines can Geoff choose from to use? Show your work or explain how you got your answer.

13. List the sample space for flipping a two-sided coin two times.

Answer 1

Answer:

1.D

2.A

3.A

4.D

5.D

6.B

7.B

8.D

9.B

10.B

11.840.

12.165

13.{H,H},{H,T},{T,H},{T,T}

Step-by-step explanation:

1.The total outcomes for this event was that Marcus could've picked ANY ONE of the tokens. So total outcomes is the total number of tokens:

$10+8+12=30$

2.Since the first draw is green, the number of FAVORABLE outcomes is the thing we got, which is green. How many green tokens were there? And, how many green tokens were possible? 8

3.The probability of picking a pair of red socks is picking up 2 red socks. So we need 1 red sock AND another red sock. The word AND means "multiply" in probability.

• The total socks is $5+2+3=10$. There are 5 red socks. The first one red sock picking probability is $\frac{5}{10}$

• Now that 1 red sock is picked, there are 4 red socks left and a total of 9 socks left. So picking another red sock now will have probability of $\frac{4}{9}$.

Multiplying these 2 gives us, $\frac{5}{10}*\frac{4}{9}=\frac{2}{9}$

4.Experimental probability is based on what happened, not what should've happened according to theory. So 32 heads appeared out of 50, the experimental probability is 32 out of 50, so on next flip it will still have same experimental probability. So, $\frac{32}{50}=0.64$

Multiplying by 100 gives the percentage: $0.64*100=64$ percent.

5.The odds of the event is given as favorable outcomes divided by non-favorable outcomes.

Since probability is $\frac{3}{10}$, the favorable outcome is 3 and non-favorable outcome is 7 (since total is 10 and 3 is favorable, 10 - 3 =7 will be non-favorable)

The odds is thus $\frac{3}{7}$

6.

• There are 10 person in total, so the first place can be taken by any one of the 10 people.
• 1 person gone, now there are 9 more people to take the 2nd place.
• 2 person gone, now there are 8 more people to take the 3rd place.

So the number of different outcomes is the product of each of these, so,

$10*9*8=720$

7.Experimental probability answer doesn't affect the theoretical probability. Since a coin has 2 sides, 1 head and another tail -- the chance of getting a head on a flip is $\frac{1}{2}$ regardless what was gotten in the experiment.

$\frac{1}{2}=0.5$

Multiplying by 100 gives the percentage: $0.5*100=50$ percent

8.The fundamental counting principle tells us that the way we can get one event and the number of ways we can get another event is the multiplication of them.

Combination is numbers of ways to pick $r$ things from a total of $n$ things. It is given by the formula:

$_{n}C_{r}=\frac{n!}{(n-r)!r!}$

• So, how many ways can we select 1 entree from 8 available?

$_{8}C_{1}=\frac{8!}{(8-1)!1!}=8$

• How many ways to select 1 dessert from 5 available?

$_{5}C_{1}=\frac{5!}{(5-1)!1!}=5$

According to the fundamental counting principle, we multiply 5 and 8 to get our answer, $5*8=40$ specials available to choose from.

9.The odds of an event is the favorable outcomes divided by the non-favorable outcomes.

• There are 30+20=50 soda cans in total

• We want green, so favorable outcomes is the number of green soda cans, which is 20.

• Number of non-favorable outcomes is NOT GREEN, there are 30 red. So non-favorable is 30.

According to rule of odds of an event, we have: $\frac{20}{30}=\frac{2}{3}$

10.We want probability of getting heads AND an even number.

AND in probability problems mean multiplication. So we multiply the probability of heads and probability of even number.

• Probability of getting heads in a coin flip is  $\frac{1}{2}$ (there are 1 heads and 1 tail, so 1 head over total outcomes, which is 2)
• Probability of getting an even number in a dice throw is $\frac{3}{6}=\frac{1}{2}$ (the numbers in a dice is 1-6, of which 3 is even, hence the probability of half)

Now multiplying gives us: $\frac{1}{2}*\frac{1}{2}=\frac{1}{4}$

11.INNOVATIVE has 7 distinct letters (there are 2 n's, 2 i's, and 2 v's -- we disregard counting twice).

The number of Permutations of $n$ objects taken $r$ at a time is given by:

$_{n}P_{r}=\frac{n!}{(n-r)!}$

For our problem, we will take 7 objects 4 at a time, putting it in the formula we have:

$_{7}P_{4}=\frac{7!}{(7-4)!}=840$

The number of permutations possible is 840.

12.Combination is numbers of ways to pick $r$ things from a total of $n$ things. It is given by the formula:

$_{n}C_{r}=\frac{n!}{(n-r)!r!}$

How many combination are possible? (We have to pick 3 items from 11 available)

$_{11}C_{3}=\frac{11!}{(11-3)!3!}=165$

165 different combinations are possible.

13.Sample space is the total possible outcomes.

When 2 coins are tossed, we can have 1 head and 1 tail from one coin & 1 head and 1 tail from another coin.

So we have a total of 4 possibilities/outcomes.

We can write the sample space as:

{H, H}, {H, T}, {T, H}, and {T, T}

Answer 2

Answer:

1.D

2.a

3.a

4.d

5.b

6.b

7.b

Step-by-step explanation: