5 - Probability Formulas

Question 1

A or B
DEPENDENT

Answer 1

A + B - (A and B)
Where A and B = A × B|A

Question 2

A or B
(MUTUAL)

Answer 2

A + B
(A and B would equal 0)

Question 3

A and B
(INDEPENDENT)

Answer 3

A × B
- ONLY if problem makes it obvious that it’s independent

Question 4

A or B
(INDEPENDENT)

Answer 4

A + B - (A and B)
Where A and B = A × B

Question 5

A | B

Answer 5

(A and B) ÷ B
- rules for independent and dependent intersection apply
- knowing it’s independent and you multiply, the B in numerator and denominator would cancel out, leaving you with A

Question 6

How to check if probabilities independent?

Answer 6

A = A | B
- B wouldn’t affect A’s outcome if it’s independent
- No match = Dependent

Question 7

A and B
DEPENDENT

Answer 7

A × (B | A)

Question 8

Difference between independent and dependent union (OR)

Answer 8

Calculating the AND is different
Independent: A × B
Dependent: A × B|A

Question 9

INDEPENDENT examples

Answer 9

• flipping coin
• Rolling die
• Anything that has replacements

Question 10

DEPENDENT examples

Answer 10

• Drawing cards from deck (with no replacement)
• choosing two kids out of a pool (cant choose same kid twice)
• Does outcome from first trial affect the outcome from the next?
• trials with no replacement
• implication of A|B

Question 11

At least 1

Answer 11

1 - complement

Question 12

At least 1 (multiple trials)

Answer 12

1 - complement^trials

Question 13

P of independent trials (replacement)
ALL OUTCOMES and NEXT OUTCOME
Ex. Flipping a coin

Answer 13

ALL: ( event ÷ all events )^trials
NEXT: ( events ÷ all events )

Question 14

P of dependent trials (no replacement)
Ex. Choosing 2 separate children from a pool to do a task

Answer 14

( event ÷ outcome ) * (event-1 ÷ outcome-1) * etc….