Algebra 1 Common Core Answers Chapter 12 Data Analysis and Probability Exercise 12.8
Algebra 1 Common Core Solutions
Chapter 12 Data Analysis and Probability Exercise 12.8 1CB
Chapter 12 Data Analysis and Probability Exercise 12.8 1LC
Consider five cards: in which 3 cards are yellow color, and two cards are red color Out o13 yellow 2 cards are mark with number 5 and 10. and one card is mark with letter B Out 012 red card one card mark with letter D. and other card is number card Therefore. 3 cards are number cards, one is red color and other two are yellow color Two cards are letter cards one is yellow color and other is red color
Chapter 12 Data Analysis and Probability Exercise 12.8 2CB
Chapter 12 Data Analysis and Probability Exercise 12.8 2LC
Chapter 12 Data Analysis and Probability Exercise 12.8 3CB
Chapter 12 Data Analysis and Probability Exercise 12.8 3LC
Consider five cards: in which 3 cards are yellow color and two cards are red color Out 013 yellow 2 cards are mark with number 5 and 10. and one card is mark with letter B. Out of 2 red card one card mark with letter D. and other card is number card.
Therefore, 3 cards are number cards, one is red color and other two are yellow color Two cards are letter cards one is yellow color and other is red color.
Chapter 12 Data Analysis and Probability Exercise 12.8 4CB
Chapter 12 Data Analysis and Probability Exercise 12.8 4LC
First, define the compound event, and then overlapping events.
Compound event: If an event consist two or more events, they are combined with the word arid or the word or.
Overlapping events: In the two or more events, if at least one event is common in each events. The example of compound event, composed of two overlapping events when you spin a spinner with integers from 1 to 28 is: The spinning numbers on spinner which is multiple of both 2 and 3. The number which is multiple of both 2 and 3 is 6. which comes when spinner is spinning and lies between the integers 1 to 8
Chapter 12 Data Analysis and Probability Exercise 12.8 5CB
Chapter 12 Data Analysis and Probability Exercise 12.8 5LC
The event and its compound event are mutually exclusive.
First define the mutually exclusive and complements of events, then explain whether an event and its complements are mutually exclusive. Mutually exclusive event: Two events are said to be mutually exclusive if the outcomes both event are not common Complement of an event consist all the outcomes of the sample space that are not in the event. To explain an event and its complement are mutually exclusive. consider an example of thronging a cube contain 6 faces are number from I to 6 Thronging a cube coming even number on its face, the complement of even number in is odd number of in the face of cube. Both are mutually exclusive events, since at time only one number is seen in the face of cube, it is either even or odd. Therefore, the even number on the face of cube and its complement odd number on the face of cube are mutually exclusive events.
Chapter 12 Data Analysis and Probability Exercise 12.8 6CB
Chapter 12 Data Analysis and Probability Exercise 12.8 6LC
First define the independent event:
Independent Event: Two events are said to be independent, if the occurrence of first event does not affect the probability of the second event
Example: A cube contains 6 faces are number from 1 to 6. Thronging a cube coming even number on its face or odd number on its face are independent event. because the occurrence of even number on the face of cube does not affect the probability of odd number on the face of cube.
Chapter 12 Data Analysis and Probability Exercise 12.8 7CB
Chapter 12 Data Analysis and Probability Exercise 12.8 7LC
Chapter 12 Data Analysis and Probability Exercise 12.8 8CB
Chapter 12 Data Analysis and Probability Exercise 12.8 8E
Chapter 12 Data Analysis and Probability Exercise 12.8 9CB
Chapter 12 Data Analysis and Probability Exercise 12.8 9E
Consider spin of a spinner A spinner is divided into 10 equal sections each section is mark with unique number with Ito 10. the number mark in one section. not repeated with other section number with 1 to & The sections mark with number 1. 2. 8. 9. and 10 are colored with blue, and the section mark with numbers 3. 4. 5. 6. and J are colored with red. That is five sections are colored with blue and five sections are colored with red
Chapter 12 Data Analysis and Probability Exercise 12.8 10CB
Chapter 12 Data Analysis and Probability Exercise 12.8 10E
Consider spin of a spinner A spinner is divided into lo equal sections each section is mark with unique number with 1 to 10, the number mark in one section, not repeated with other section number with I to 6. The sections mark with number 1. 2. 8. 9. and 10 are colored with blue, and the section mark with numbers 3. 4. 5. 6. and 7 are colored with red. That is five sections are colored with blue and five sections are colored with red.
Chapter 12 Data Analysis and Probability Exercise 12.8 11CB
Chapter 12 Data Analysis and Probability Exercise 12.8 11E
Chapter 12 Data Analysis and Probability Exercise 12.8 12CB
Chapter 12 Data Analysis and Probability Exercise 12.8 12E
Chapter 12 Data Analysis and Probability Exercise 12.8 13CB
Consider the statement given in the question:
The required tree diagram has been drawn below using the information given in the question:
As. y is also included, so the total outcome for the last letter = 6
And, the total number of alphabets = 26
Chapter 12 Data Analysis and Probability Exercise 12.8 13E
Chapter 12 Data Analysis and Probability Exercise 12.8 14E
Chapter 12 Data Analysis and Probability Exercise 12.8 15E
Chapter 12 Data Analysis and Probability Exercise 12.8 16E
Chapter 12 Data Analysis and Probability Exercise 12.8 17E
Consider the following statement,
You roll a blue number cube and a green number cube.
To find the probability P (blue even and green even):
Chapter 12 Data Analysis and Probability Exercise 12.8 18E
Chapter 12 Data Analysis and Probability Exercise 12.8 19E
Chapter 12 Data Analysis and Probability Exercise 12.8 20E
Chapter 12 Data Analysis and Probability Exercise 12.8 21E
Chapter 12 Data Analysis and Probability Exercise 12.8 22E
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Chapter 12 Data Analysis and Probability Exercise 12.8 28E
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Chapter 12 Data Analysis and Probability Exercise 12.8 31E
Chapter 12 Data Analysis and Probability Exercise 12.8 32E
Chapter 12 Data Analysis and Probability Exercise 12.8 33E
Consider the following data:
- In a set of nine coins 3 nickel. 3 dime, 2 penny. and one quarter
- One coin is picked randomly from set of coins
- Second coin is picked without replacing first
Objective is to find the probability P(quarter after quarter). Here, the second coin is picked without replacing the first So, the number of coins for second choice is less than one. This means that, to pick the first coin is affecting the probability to pick the second coin, so both the events are dependent.
Chapter 12 Data Analysis and Probability Exercise 12.8 34E
Consider the following data:
- There are total 5 friends, they are: You, T. and 3 other friends.
- Every day one name is chosen from a hat contains these 5 friends names.
Objective is to find the probability that you are chosen on Monday and T is chosen on Tuesday.
This can be mathematically expressed as find the probability P(You then T).
Total there are 5 friends including you and T
To select your name first then T are dependent events. because to select first event affect the probability of second events.
Chapter 12 Data Analysis and Probability Exercise 12.8 35E
Consider the following data:
- A new drink samples contains 5 citrus drinks. 3 apple drinks, and 3 raspberries drink.
- In total. there are 11 drinks.
Objective is to find the probability that an apple drink and then a citrus drink are handed out.
This can be mathematically expressed as:
Find the probability P (apple drink then citrus drink).
To hand out apple drinks then citrus drink are dependent events: because when a apple drink is handed out then the number of drinks is one less than the previous drinks. So the outcomes of first event affect the probability of second event.
Chapter 12 Data Analysis and Probability Exercise 12.8 36E
Consider the following events:
- Event 1: Toss a penny.
- Event 2: Then toss a nickel
Objective is to determine whether the two events are dependent or independent.
Dependent events: If the probability of second event is affected by the occurrence of first event, then the two events are said to be dependent. Independent events If the probability of second event does not affected by the occurrence of first event, then the two events are said to be independent Here, if one toss a penny. then coming any one face out of two faces on the penny. does not affect the coming any faces out of two faces on nickel. This means. the occurrence of first event that is tossing a penny does not affect the probability of the second event that is the probability of nickel So. tossing penny and nickel are gives the different outcome. Therefore, toss a Penny and then toss a nickel are independent events.
Chapter 12 Data Analysis and Probability Exercise 12.8 37E
Consider the following events:
- Event 1: Pick a name from a hat
- Event 2: without replacement pick a different name is dependent event
Objective is to determine whether the two events are dependent or independent.
Dependent events: If the probability of second event is affected by the occurrence of first event. then the two events are said to be dependent Independent events If the probability of second event does not affected by the occurrence of first event, then the two events are said to be independent
Chapter 12 Data Analysis and Probability Exercise 12.8 38E
Consider the following events:
- Event 1: Pick a ball from a basket of yellow and pink balls
- Event 2: Returned the first ball and pick the second one.
Objective is to determine whether the two events are dependent or independent
Dependent events If the probability of second event is affected by the occurrence of first event, then the two events are said to be dependent
Independent events: If the probability of second event does not affected by the occurrence of first event, then the two events are said to be independent Here, pick a ball from a basket of yellow and pink balls. and then retuned back to basket before second ball is drawn. So. the numbers of ball in basket are same as first drawn for the second time Therefore, the occurrence of first event does not affect the probability of the second Thus, pick a ball from a basket of yellow and pink balls. Returned the first ball and pick second is independent event
Chapter 12 Data Analysis and Probability Exercise 12.8 39E
Consider the following events:
- Event 1: Pick a ball from a basket of yellow and pink balls.
- Event 2: Returned the first ball and pick the second one
Objective is to determine whether the two events are dependent or independent
Dependent events: If the probability of second event is affected by the occurrence of first event, then the two events are said to be dependent
Examples: Select a card from a pack of card contain 52 cards, first card is not replaced in the pack and second card is drawn from a pack.
Independent events: If the probability of second event does not affected by the occurrence of first event, then the two events are said to be independent Examples Tossing two coins, coming head or tails on first coin does not affect the probability of coming head or tails on second coin Rolling two dice contain the number from I to 6. Coming any number from I to 6 on first dice does not affect the coming any number on the second dice
Chapter 12 Data Analysis and Probability Exercise 12.8 40E
Consider the statement given in the question:
Total number of mint is 20 + 80 = 1oo
Let the green mint be x
So. the pink mint is 8O—x
Chapter 12 Data Analysis and Probability Exercise 12.8 41E
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Chapter 12 Data Analysis and Probability Exercise 12.8 46E
Chapter 12 Data Analysis and Probability Exercise 12.8 47E
Chapter 12 Data Analysis and Probability Exercise 12.8 48E
Consider the statement given in the question:
For the boys from the wrestling team the cafeteria will not be a good option for them as they require more nutritious food to eat and maintain their diet. But for the homeroom they will prefer the cafeteria more as they are already having healthy food at home so. they will want the cafeteria food products more. Thus, the result will vary for both of them
b.
The question for the pizza favor is given below:
What is your favorite topping on the pizza?
The question about the menu choices that is baised is given below:
Would you prefer a cheese burst pizza or a thin crust pizza?
Chapter 12 Data Analysis and Probability Exercise 12.8 49E
Chapter 12 Data Analysis and Probability Exercise 12.8 50E
Chapter 12 Data Analysis and Probability Exercise 12.8 51E
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Chapter 12 Data Analysis and Probability Exercise 12.8 53E
Chapter 12 Data Analysis and Probability Exercise 12.8 54E
Chapter 12 Data Analysis and Probability Exercise 12.8 55E
