Probability

Question 1

What is probability?

Answer 1

success / attempts

Question 2

Random meaning

Answer 2

• every individual event is unpredictable

- the overall pattern is completely predictable

Question 3

P(A)

Answer 3

Probability of A

Question 4

P(not A)

Answer 4

1 - P(A)

Question 5

Approximate rules

Answer 5

"or" = add 
"and" = multiply

Question 6

Generalized rule P(A or B)

Answer 6

= P(A) + P(B) - P(A & B)

Question 7

What does mutually exclusive?

Answer 7

• means that its disjoint
• its impossible for both A and B to happen at the same time
• possibilities:
  a. A happens
  b. B happens
  c. neither A or B

P(A and B) = 0
used in dice, coins, cards

Question 8

If A and B aren’t mutually exclusive…

Answer 8

A and B can happen together

Question 9

What are independent events?

Answer 9

2 events that have no effect on each other

Question 10

with replacement vs without replacement

Answer 10

with replacement:
- whatever choice happens, the choice is placed back in the pile
- each choice comes from newly randomized collection
without replacement:
- each choice comes from a smaller collection

Question 11

What is the generalized “And” rule?

Answer 11

P(A & B) = P(A) x (P(A | B) )

= P(B) x (P(B | A) )

Question 12

What are independent events?

Answer 12

2 events that have no effect on each other

Question 13

Define the binomial situation:

Answer 13

• probability of success is given or obvious
• # trials n is decided beforehand
• what is the probability of r successes in n trials

Question 14

When are conditions of “mutually exclusive” and “independent” most common?

Answer 14

Most common with dice, coins, cards, etc.

Question 15

T/F Selection processes that are without replacement are never independent

Answer 15

TRUE

Question 16

Suppose we roll a six-sided die 8 times. What is the probability that we will roll at least one six?

Answer 16

Need to think about it using combination formula: 
At least one 6 includes: 
1 six 
2 sixes 
3 sixes 
4 sixes 
5 sixes 
6 sixes 
7 sixes 
exactly 8 sixes 
out of 9 possibilities

But you can use the complement rule here:
- probability that it’s not a 6 is 5/6
1 - (5/6)^8 = 0.76

Question 17

When should you use the complement rule?

Answer 17

When there is a question contains an “at least scenerio”

Question 18

In a class of 40 students, 12 are left-handed and the other 28 are right-handed. If two students are chosen at random, what’s the probability that one is left-handed and one is right-handed?

How do you approach this problem

Answer 18

Count the number of ways to get a L and R handed choice
LL
RR
LR
RL 
2 ways out of 4 

Solve for the specific probability of each of the two scenarios. Know that selections are not independent and there is no replacement.