Show:
Vocabulary
Theoretical/Experimental
Independent Events
Dependent Events
Populations & Sample
100
What makes a sample bias?
The outcomes are not equally likely to occur. There is a prejudice that will make our sample not represent the population.
100
What is the theoretical probability of rolling an odd number on a 6-sided di?
3/6 = 1/2
100
I have 10 marbles in a bag: 5 blue, 3 green, 1 yellow, and 1 purple. If I take a marble, record the color and replace it, then choose another marble, what is the probability I will choose a blue marble then a green marble?
P(blue)=5/10 P(green)=3/10 P(blue,green)= .5*.3 = .15 or 15%
100
I have 5 markers in a bag; 3 blue and 2 red. If I choose 1 marker, place it on my desk then choose another, what is the probability I will choose a blue marker then another blue marker?
P(blue)=3/5 P(blue 2)=2/4 P(blue, blue 2) = 3/5 * 2/4 = 6/20 = 30%
100
MH2 must hire a DJ for the 8th grade band. We want to know which music genre the 8th graders prefer. We ask every 5th student who walks into each homeroom what music they prefer. What is the population?
The 8th grade class.
200
What makes a sample random?
-Each outcome is equally likely to occur
200
There are 10 marbles in a bag, 4 red, 3 blue, 2 green, and 1 yellow. What is the theoretical probability you will choose a green marble?
2/10 = 1/5
200
I have 10 marbles in a bag: 5 blue, 3 green, 1 yellow, and 1 purple. If I take a marble, record the color and replace it, then choose another marble, what is the probability I will choose a yellow marble then a purple marble?
P(yellow)=1/10 P(purple)=1/10 P(yellow,purple)= .1*.1 = .01 or 1%
200
I have 5 markers in a bag; 3 blue and 2 red. If I choose 1 marker, place it on my desk then choose another, what is the probability I will choose a blue marker then a red marker?
P(blue,red)= 6/20 = 30%
200
MH2 must hire a DJ for the 8th grade band. We want to know which music genre the 8th graders prefer. We ask every 5th student who walks into each homeroom what music they prefer. Who is the sample?
Every 5th student in each homeroom
300
Define Independent events.
Events that do not affect one another.
300
There are 5 marbles in a bag, 3 black and 2 white. If we were to pick a marble, replace it, and repeat this process for 150 trials, how many black marbles would you expect to choose?
90 black marbles.
300
I have a spinner with 4 equal sections: blue, green, yellow, and red and a 6-sided di. If I spin and then roll the di, what is the probability I will get yellow and an even number?
P(yellow)=1/4 P(even)=1/2 P(yellow,even)=1/4 * 1/2 = 1/8 or 12.5%
300
Student council is made up of 13 students; 5 boys and 8 girls. They will randomly choose president and vice president by picking names out of a hat. What is the probabilty both the president and vice president are girls?
P(girl, girl) = 56/156 = 36%
300
MH2 must hire a DJ for the 8th grade band. We want to know which music genre the 8th graders prefer. We ask every 5th student who walks into each homeroom what music they prefer. Is this bias or random? Explain.
This is random because each student is equally likely to be chosen.
400
Define dependent events
Events where the outcome of the first event affects the outcome of the second event.
400
The experimental probability of rolling a 4 on a 6-sided di was 12/50. Explain what this means.
After rolling a 6-sided di 50 times, 4 showed up 12 times.
400
Student council is made up of 13 students; 5 boys and 8 girls. They will randomly choose president and vice president by picking names out of a hat. What is the probabilty both the president and vice president are boys?
P(boy, boy) = 20/156 = 13%
400
Polls were taken outside the 1, 2, A and C subway stops. It was found that 55% of people polled spent at least 30 minutes a day on the subway. They concluded that 55% of New Yorkers spent at least 30 minutes a day on the subway. State the population and sample.
Population: New Yorkers Sample: people polled getting off the 1,2,A and C subway
500
Define the complement of an event.
The probability of that event NOT happening.
500
For lunch I can choose one drink, one sandwich, and one dessert. I can drink water or milk, my sandwich choices are turkey, ham, or beef, and for dessert I can have cookies or ice cream. Each option is equally likely to be chosen. What is the probability my meal will include a beef sandwich and ice cream?
P(beef)=1/3 P(ice cream)=1/2 P(beef, ice cream)=1/3 * 1/2 = 1/6
500
Polls were taken outside the 1, 2, A and C subway stops. It was found that 55% of people polled spent at least 30 minutes a day on the subway. They concluded that 55% of New Yorkers spent at least 30 minutes a day on the subway. Is this a random sample or bias sample? Explain.
This is bias because they are only asking New Yorkers who are getting off the subway; these residents are more likely to spend time on the subway. Not every New Yorker had an equally likely chance of being polled.