Lab #5 - Meghan Wright Exercise #1: -Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure". - What is the probability of getting heads or tails? 50% - From your graph does it appear that there is any bias in the coin? No
Runs in 100 flips of a coin:
Heads
Tails
2X = 9
2X= 7
3X = 6
3X= 5
4X = 2
4X = 3
5X = 1
5X = 0
6X= 0
6X= 0
7X= 0
7X= 0
8X= 0
8X= 0
Frequency of Runs in 100 Flips of a Coin Exercise #2: -An experiment is a situation involving chance or probability that leads to results called outcomes, i.e. rolling a die. -An outcome is the result of a single trial of an experiment, i.e. there are 6 possible outcomes of rolling a die. -An event is one or more outcomes of an experiment, i.e. rolling a 5 is a possible event - Probability is the measure of how likely an event is, i.e. the probability of rolling each number on a die is 1/6th. - What are all the possible "events" when rolling a dice? 1
- What are all the possible "outcomes" when rolling a dice? 6
- In 100 throws of the dice what is the probability that each number (outcomes) will occur? 16.7% - Is there any evidence that the dice was loaded? No.
Outcomes of rolling a dice:
Outcomes/ -> total # events
1
10
2
17
3
21
4
14
5
23
6
15
Exercise #3: Experiment Results:
2 heads
2
2 Tails
3
1 head + 1 tail
5
Probability of results:
2 Heads
1
2 tails
1
1 head + 1 tail
2
What percentage of the time is the outcome 2 heads? 1/4 What percentage of the time is the outcome 2 tails? 1/4 What percentage of the time is the outcome 1 head,1 tail? 2/4
Explain how you would calculate the probability for these results: there are two possible outcomes from flipping one coin and two possible outcomes for flipping the other, by flipping both there are 4 possible outcomes than can occur when flipping the two together. Therefore the probability of one event occurring out of the 4 possible outcomes is 1/4.
Exercise #4:
What is the probability of each outcome for 1 dice? 1/6 What is the probability of each outcome for 2 dice? 1/36
1 (1/6)
2 (1/6)
3 (1/6)
4 (1/6)/ 5, 6, & 7->
1 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
2 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
3 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
4 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
5 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
6 (1/6)
1/36
1/36
1/36
1/36
1/36
1/36
1/36
The calculated probability of getting the following (sums of individual outcomes)
2
3
4
5
6
7
8
9
10
11 &12
1/18
1/18
1/18
1/9
1/9
1/6
1/6
1/9
1/9
1/18
1/18
The measured frequency of getting the following in an experiment of 100 rolls
Exercise #1:
-Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure".
- What is the probability of getting heads or tails? 50%
- From your graph does it appear that there is any bias in the coin? No
Runs in 100 flips of a coin:
Exercise #2:
-An experiment is a situation involving chance or probability that leads to results called outcomes, i.e. rolling a die.
-An outcome is the result of a single trial of an experiment, i.e. there are 6 possible outcomes of rolling a die.
-An event is one or more outcomes of an experiment, i.e. rolling a 5 is a possible event
- Probability is the measure of how likely an event is, i.e. the probability of rolling each number on a die is 1/6th.
- What are all the possible "events" when rolling a dice? 1
- What are all the possible "outcomes" when rolling a dice? 6
- In 100 throws of the dice what is the probability that each number (outcomes) will occur? 16.7%
- Is there any evidence that the dice was loaded? No.
Outcomes of rolling a dice:
Exercise #3:
Experiment Results:
Probability of results:
What percentage of the time is the outcome 2 heads? 1/4
What percentage of the time is the outcome 2 tails? 1/4
What percentage of the time is the outcome 1 head,1 tail? 2/4
Explain how you would calculate the probability for these results: there are two possible outcomes from flipping one coin and two possible outcomes for flipping the other, by flipping both there are 4 possible outcomes than can occur when flipping the two together. Therefore the probability of one event occurring out of the 4 possible outcomes is 1/4.
Exercise #4:
What is the probability of each outcome for 1 dice? 1/6
What is the probability of each outcome for 2 dice? 1/36
The calculated probability of getting the following (sums of individual outcomes)
Possible sums of 2 rolled die