Basic Probability Rules
Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint (mutually exclusive), then the probability that either events occur is
0.90
P(A|B)= _____
P(A and B)/ P(B)
Three machines – A, B, and C – are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
How many outcomes are possible for this sample space?
6 outcomes
What is a simulation?
A model of a chance outcome.
A counselor analyzes student’s course selection and calculates the following: The probability that a randomly-chosen student is taking Spanish is 0.4, that the student is taking Chemistry is 0.3, and that the student is taking BOTH Chemistry and Spanish is 0.1
What is the probability that a student is NOT taking Spanish?
0.60
Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint (mutually exclusive), then the probability that both events occur is
0
In a cookie jar, there are 12 chocolate chip cookies, 5 oatmeal raison cookies, and 7 macadamia nut cookies. What is the probability that if two cookies were chosen (without replacement), that both cookies were chocolate chip?
0.24
Three machines – A, B, and C – are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
List the outcomes:
Machine A and defective
Machine A and NOT defective
Machine B and defective
Machine B and NOT defective
Machine C and defective
Machine C and NOT defective
Describe how you would use Table D to randomly select 5 students from the class.
Assign each student a number from 1 to n
Choose a random line in table D and mark off groups of two numbers consecutively to represent the students you are selecting.
Repeat numbers not allowed, skip any numbers outside the range above.
Select 5 unique numbers that represent the students you will select.
A counselor analyzes student’s course selection and calculates the following: The probability that a randomly-chosen student is taking Spanish is 0.4, that the student is taking Chemistry is 0.3, and that the student is taking BOTH Chemistry and Spanish is 0.1
What is the probability that a student is NOT taking Chemistry?
0.70
Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur is
0.20
An event A will occur with probability 0.5. An event B will occur with probability 0.4. The probability that both A and B will occur is 0.2. The conditional probability of A, given B is
Responses
0.50
Three machines – A, B, and C – are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
What is the probability that a randomly chosen part was made by Machine A and IS defective?
0.06
Describe how you would use technology to select 5 random students from the class.
Assign each student a number from 1 to n
Go to RANDINT in the calculator and have it select random numbers between 1 and n.
Repeat numbers not allowed, skip any numbers outside the range above.
Select 5 unique numbers that represent the students you will select.
A counselor analyzes student’s course selection and calculates the following: The probability that a randomly-chosen student is taking Spanish is 0.4, that the student is taking Chemistry is 0.3, and that the student is taking BOTH Chemistry and Spanish is 0.1
Create a Venn Diagram
Review Answer
When rolling a fair die, you roll a 6 four times in a row. Given that each roll is independent, what is the probability that the next roll yields a six also?
(1/6)^5
or
0.00013
The probability that it will Rain on a given day is 0.40.
The probability that a student will be late to school on that day that it rains is 0.35
What is the probability that a student is late given that it rains?
0.875
Three machines – A, B, and C – are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
What is the probability that a randomly chosen part is defective GIVEN that it was made on machine A?
0.10
Describe law of large numbers and what it means.
You need many, many trials to estimate the probability with the most accuracy to the theoretical probability.
Short term probability is NOT predictable. Long term probability is predictable.
A counselor analyzes student’s course selection and calculates the following: The probability that a randomly-chosen student is taking Spanish is 0.4, that the student is taking Chemistry is 0.3, and that the student is taking BOTH Chemistry and Spanish is 0.1
What is the probability that a randomly selected student is NOT taking Chemistry or Spanish?
0.40
Ignoring twins and other multiple births, assume that babies born at a hospital are independent random events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.
What is the probability that the next 3 babies born are girls?
0.125
P(Rain | Late) = 0.70
P(Late)= 0.43
P(Rain) = 0.54
P(Rain and Late) = ?
0.301
Three machines – A, B, and C – are used to produce a large quantity of identical parts at a factory. Machine A produces 60% of the parts, while Machines B and C produce 30% and 10% of the parts respectively. Historical records indicate that 10% of the parts produced by Machine A are defective, compared with 30% for Machine B and 40% for Machine C.
What is the probability that a randomly chosen part was made on machine A, GIVEN that it is defective?
0.06 / 0.19 = 0.32
Assuming that the probability that it will rain any day next week is 20%, use a simulation to estimate the probability that it will rain on exactly 3 out of the 7 days next week. Use at least 10 trials. Show your work. (This is the DO Step)
Answers will vary.
A counselor analyzes student’s course selection and calculates the following: The probability that a randomly-chosen student is taking Spanish is 0.4, that the student is taking Chemistry is 0.3, and that the student is taking BOTH Chemistry and Spanish is 0.1
What is the probability that a randomly selected student is taking Spanish OR Chemistry?
0.60