Basic Probability
If you roll a single fair die and count the number of dots on top, what is the probability of getting a number greater than 3 on a single throw?
P(>3)=2/3
A random sample of 317 new Smile Bright electric toothbrushes showed that 19 were defective. How would you estimate the probability that a new Smile Bright electric toothbrush is defective?
Relative frequency
You roll two fair dice, a blue one and a yellow one. Find P(even number on the blue die and 3 on the yellow die).
P(even number on the blue die and 3 on the yellow die)=1/12
A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results below. What is the probability a customer is unsatisfied?
| Walk-in| Tv Ad| Referred| Total ________________________________________
Not satisfied | 21 | 9 | 5. | 35
Neutral | 18 | 25 | 37 | 80
Satisfied | 36 | 43 | 59 | 138
Very Satisfied | 28 | 31 | 48 | 107
______________________________________
Total. | 103 | 108 | 149 | 360
P(unsatisfied)=35/360
In how many different ways can a student choose three of eight problems to complete on a take-home exam?
56
If you roll a single fair die and count the number of dots on top, what is the probability of getting a number less than or equal to 5 on a single throw?
P(<5)=5/6
A random sample of 317 new Smile Bright electric toothbrushes showed that 19 were defective. What is your estimate?
P(defective)=19/317
You roll two fair dice, a blue one and a yellow one. Find P(3 on the blue die and even number on the yellow die).
P(3 on the blue die and even number on the yellow die)=1/12
A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results below. What is the probability a customer is not satisfied, given that he or she was referred?
?
| Walk-in| Tv Ad| Referred| Total ________________________________________
Not satisfied | 21 | 9 | 5. | 35
Neutral | 18 | 25 | 37 | 80
Satisfied | 36 | 43 | 59 | 138
Very Satisfied | 28 | 31 | 48 | 107
______________________________________
Total. | 103 | 108 | 149 | 360
P(not satisfied, given that he or she was referred)=5/149
George has four ties, three shirts, and two pairs of pants. How many different outfits can he wear if he chooses one tie, one shirt, and one pair of pants for each outfit?
(4)(3)(2)=24
If you roll a single fair die and count the number of dots on top, what is the probability of getting an even number on a single throw?
P(even #)=1/2
A random sample of 317 new Smile Bright electric toothbrushes showed that 19 were defective. What is your estimate for the probability that a Smile Bright electric toothbrush is not defective?
P(Not defective)=1-(19/317)=298/317
You roll two fair dice, a blue one and a yellow one. Find P(even number on the blue die and 3 on the yellow die) or P(3 on the blue die and even number on the yellow die).
P(even number on the blue die and 3 on the yellow die) or P(3 on the blue die and even number on the yellow die)=1/12+1/12=1/6
A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results below. What is the probability a customer is very satisfied?
| Walk-in| Tv Ad| Referred| Total ________________________________________
Not satisfied | 21 | 9 | 5. | 35
Neutral | 18 | 25 | 37 | 80
Satisfied | 36 | 43 | 59 | 138
Very Satisfied | 28 | 31 | 48 | 107
______________________________________
Total. | 103 | 108 | 149 | 360
P(very satisfied)=107/360
In how many ways can the 40 members of a 4H club select a president, a vice president, a secretary, and a treasurer?
40•39•38•37 = 2,193,360
If you pull a marble out of an urn that has 3 red marbles, 2 green and 1 yellow. What is the probability of getting a red marble?
P(Red)=1/2
A random sample of 317 new Smile Bright electric toothbrushes showed that 19 were defective.What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1?
Defective, Not Defective; yes they equal 1.
An urn contains 12 balls identical in every respect except color. There are 3 red balls, 7 green balls, and 2 blue balls. You draw two balls from the urn but replace the first ball before drawing the second. Find the probability that the first ball is red and the second is green.
P( the first ball is red and the second is green)=(3/12)(7/12)=7/48
A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results below. What is the probability a customer is very satisfied and TV ad?
| Walk-in| Tv Ad| Referred| Total ________________________________________
Not satisfied | 21 | 9 | 5. | 35
Neutral | 18 | 25 | 37 | 80
Satisfied | 36 | 43 | 59 | 138
Very Satisfied | 28 | 31 | 48 | 107
______________________________________
Total. | 103 | 108 | 149 | 360
P(very satisfied and TV ad)=48/149
In how many different ways can a person choose three movies to see in a theater playing 11 movies?
C11,3=165
If you pull a marble out of an urn that has 3 red marbles, 2 green and 1 yellow. What is the probability of getting a white marble?
P(white)=0
A random sample of 420 new Ford trucks showed that 105 required repairs within the first warranty year. What is the estimate for the probability that a new Ford truck will need repairs within the first warranty year?
P(need repair)=105/420=1/4
An urn contains 12 balls identical in every respect except color. There are 3 red balls, 7 green balls, and 2 blue balls. You draw two balls from the urn but do not replace the first ball before drawing the second. Find the probability that the first ball is red and the second is green.
P(first ball is red and the second is green)=(3/12)(7/11)=21/132
A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. A walk-in customer is one who has seen no ads and not been referred. The other customers either saw a TV ad or were referred to the salon (but not both). The results below. Are the events “satisfied” and “referred” independent or not? Explain your answer with probabilities.
| Walk-in| Tv Ad| Referred| Total ________________________________________
Not satisfied | 21 | 9 | 5. | 35
Neutral | 18 | 25 | 37 | 80
Satisfied | 36 | 43 | 59 | 138
Very Satisfied | 28 | 31 | 48 | 107
______________________________________
Total. | 103 | 108 | 149 | 360
No P(referred) does not equal P(referred|satisfied)
A computer package sale comes with two different choices of printers and four different choices of monitors. If a store wants to display each package combination that is for sale, how many packages must be displayed? Make a tree diagram showing the outcomes for selecting printer and monitor.
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