4.5 comparing and selecting discrete probability
TRANSCRIPT
4.5 Comparing and Selecting Discrete Probability
Distributions.notebook1
Comparing and Selecting Discrete Probability Distributions
4.5
I am learning to • compare the probability distribuons of discrete random variables • solve problems involving uniform, binomial, and hypergeometric distribuons
I will know I'm successful when I can • disnguish between a discrete random variable and a connuous random variable • represent a probability distribuon using a table • represent a probability distribuon using a histogram • calculate the expected value of a probability distribuon • calculate the weighted mean of a probability distribuon
What are some other success criteria?
Success Criteria
2
4.5
Consider the binomial and hypergeometric distributions.
1. If you have not already done so, draganddrop the labels below on the right to complete the compare and contrast graphic organizer.
Independent
Number of trials
Number of successes
Dependent Population breakdownSample breakdown
ra/n
Criteria
Invesgate Comparing Binomial and Hypergeometric Distribuons
Comparing and Selecting Discrete Probability Distributions
4.5
2. Reflect Use your graphic organizer from step 1 to help classify each of the probability distributions as binomial, hypergeometric, or neither. Justify your classification.
a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw
Binomial Hypergeometric (drag to label each probability distribuon)
e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05%
b) the probability of a given number of rolls before rolling doubles with two dice
c) the probability of each possible outcome when a card is drawn from a standard deck
d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year
Neither
Binomial Binomial
Neither Neither
3
4.5
a) Use the frame and labels below to create a Venn diagram to compare and contrast the following probability distributions.
• cutting five cards from a standard deck, with replacement, and counting the number of face cards
• dealing five cards at the same time from a standard deck and counting the number of face cards
Cutting Cards
Dealing Cards
No replacement, so dependent trials
Binomial Hypergeometric
Event ParametersPopulation
Cards Dealing Cards
so dependent trials
# of Trials = 5
Binomial Hypergeometric
4.5
Reflect
R1. Is drawing 5 numbers from 49 for a lottery a binomial or hypergeometric distribution? Explain.
R2. Sam wrote that the difference between binomial and hypergeometric distributions is that with the binomial distribution each trial has the same probability, but with hypergeometric the individual probabilities change with the sampling. Is this an accurate statement? Explain.
A ns w er The events are dependent so
drawing for a lottery is a hypergeometric distribution.
No,Sam's statement would be more accurate if it said "with hypergeometric the individual probabilities change with the lack of replacement."
A ns w er
4
1 Use the pen tool to choose the best answer.
Which situation would be represented by a binomial distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of 50 eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
4.5
B
2 Use the pen tool to choose the best answer.
Which situation would be represented by a uniform distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of fifty eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
5
3 Use the pen tool to choose the best answer.
Which situation would be represented by a hypergeometric distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of fifty eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
questions.
6
Invesgate Comparing Binomial and Hypergeometric Distribuons
Finite Population Counting successes Random variable is the number of successes
Continuous Set number of trials
Independent Population breakdown Probability of a single trial Number of trials Number of successes np n, p, q 0 to number of trials
Dependent Population breakdown Sample breakdown Number of trials Number of successes ra/n n, r, a 0 to number available
Go back to the question
Solutions
Invesgate Comparing Binomial and Hypergeometric Distribuons 2. a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw
Binomial; the successful free throws are counted, and each free throw is independent.
Binomial; we are counng successes (number of defecve baeries) in a set number of independent trials.
Hypergeometric; trials are dependent and we are counng successes (tagged bears).
Neither; it is a single draw of a card.
Neither; even though the trials are independent, there is no set number of trials.
e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05%
d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year
c) the probability of each possible outcome when a card is drawn froma standard deck
b) the probability of a given number of rolls before rolling doubles with two dice
Go back to the question
Attachments
0
0.2693290743
0.2531812725
1
2
3
4
5
1. The Probability With Replacement column contains the following formula in B2: =COMBIN(5,A2)*(3/13)^A2* (10/13)^(5-A2) Copy it from B2 to B7. 2. The Probability Without Replacement column contains the hypergeometric formula in C2: =COMBIN(12,A2)* COMBIN(40,5-A2)/COMBIN(52,5) Copy it from C2 to C7. 3. Highlight columns B and C, select Insert from the ribbon, and then select Clustered Column. 4. Right click on the chart and click on Select Data… . 5. Under Horizontal (Category) Axis Labels, click Edit. Highlight cells A2 to A7 for the axis label range. Click OK. Click OK again.
Solution
Number of Cards
Comparing and Selecting Discrete Probability Distributions
4.5
I am learning to • compare the probability distribuons of discrete random variables • solve problems involving uniform, binomial, and hypergeometric distribuons
I will know I'm successful when I can • disnguish between a discrete random variable and a connuous random variable • represent a probability distribuon using a table • represent a probability distribuon using a histogram • calculate the expected value of a probability distribuon • calculate the weighted mean of a probability distribuon
What are some other success criteria?
Success Criteria
2
4.5
Consider the binomial and hypergeometric distributions.
1. If you have not already done so, draganddrop the labels below on the right to complete the compare and contrast graphic organizer.
Independent
Number of trials
Number of successes
Dependent Population breakdownSample breakdown
ra/n
Criteria
Invesgate Comparing Binomial and Hypergeometric Distribuons
Comparing and Selecting Discrete Probability Distributions
4.5
2. Reflect Use your graphic organizer from step 1 to help classify each of the probability distributions as binomial, hypergeometric, or neither. Justify your classification.
a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw
Binomial Hypergeometric (drag to label each probability distribuon)
e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05%
b) the probability of a given number of rolls before rolling doubles with two dice
c) the probability of each possible outcome when a card is drawn from a standard deck
d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year
Neither
Binomial Binomial
Neither Neither
3
4.5
a) Use the frame and labels below to create a Venn diagram to compare and contrast the following probability distributions.
• cutting five cards from a standard deck, with replacement, and counting the number of face cards
• dealing five cards at the same time from a standard deck and counting the number of face cards
Cutting Cards
Dealing Cards
No replacement, so dependent trials
Binomial Hypergeometric
Event ParametersPopulation
Cards Dealing Cards
so dependent trials
# of Trials = 5
Binomial Hypergeometric
4.5
Reflect
R1. Is drawing 5 numbers from 49 for a lottery a binomial or hypergeometric distribution? Explain.
R2. Sam wrote that the difference between binomial and hypergeometric distributions is that with the binomial distribution each trial has the same probability, but with hypergeometric the individual probabilities change with the sampling. Is this an accurate statement? Explain.
A ns w er The events are dependent so
drawing for a lottery is a hypergeometric distribution.
No,Sam's statement would be more accurate if it said "with hypergeometric the individual probabilities change with the lack of replacement."
A ns w er
4
1 Use the pen tool to choose the best answer.
Which situation would be represented by a binomial distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of 50 eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
4.5
B
2 Use the pen tool to choose the best answer.
Which situation would be represented by a uniform distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of fifty eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
5
3 Use the pen tool to choose the best answer.
Which situation would be represented by a hypergeometric distribution?
A Dealing 2 cards from a standard deck
B The top face showing when rolling a single die
C Drawing one letter tile from a bag of fifty eight times, with replacement.
D Recording the Probability of Precipitation (P.O.P.) for 7 days.
Comparing and Selecting Discrete Probability Distributions
Answer
questions.
6
Invesgate Comparing Binomial and Hypergeometric Distribuons
Finite Population Counting successes Random variable is the number of successes
Continuous Set number of trials
Independent Population breakdown Probability of a single trial Number of trials Number of successes np n, p, q 0 to number of trials
Dependent Population breakdown Sample breakdown Number of trials Number of successes ra/n n, r, a 0 to number available
Go back to the question
Solutions
Invesgate Comparing Binomial and Hypergeometric Distribuons 2. a) the probability of successfully shooting 13 free throws in 15 tries given the probability of success on a free throw
Binomial; the successful free throws are counted, and each free throw is independent.
Binomial; we are counng successes (number of defecve baeries) in a set number of independent trials.
Hypergeometric; trials are dependent and we are counng successes (tagged bears).
Neither; it is a single draw of a card.
Neither; even though the trials are independent, there is no set number of trials.
e) the probability that three or more batteries are defective in a batch of 35 batteries when batteries have a rate of defect of 0.05%
d) selecting 25 grizzly bears at random and determining how many of them were tagged with radio chips over the last year
c) the probability of each possible outcome when a card is drawn froma standard deck
b) the probability of a given number of rolls before rolling doubles with two dice
Go back to the question
Attachments
0
0.2693290743
0.2531812725
1
2
3
4
5
1. The Probability With Replacement column contains the following formula in B2: =COMBIN(5,A2)*(3/13)^A2* (10/13)^(5-A2) Copy it from B2 to B7. 2. The Probability Without Replacement column contains the hypergeometric formula in C2: =COMBIN(12,A2)* COMBIN(40,5-A2)/COMBIN(52,5) Copy it from C2 to C7. 3. Highlight columns B and C, select Insert from the ribbon, and then select Clustered Column. 4. Right click on the chart and click on Select Data… . 5. Under Horizontal (Category) Axis Labels, click Edit. Highlight cells A2 to A7 for the axis label range. Click OK. Click OK again.
Solution
Number of Cards