Stats Exam 2

• Multiply, independent events?
• Add, mutually exclusive?

In a sequence of events (like choosing what piece of clothes to wear), multiply the numbers together to get the total number of combinations possible.

• When order matters!
• "arrange, order, rearrange, rank, sequence, in how many ways can things be ordered"

number of permutations of n objects: n! (arrange)

• nPr= n!÷(n-r)! (selected piece and arrange them)
• n= # of objects (bigger #)
• r= selected # (smaller #)

• Order doesn't matter!
• "choose, select, team, committee"

• nCr= n!÷(n-r)!r!
• n= # of objects (bigger #)
• r= selected # (smaller #)

• 1
• 1 1
• 1 2 1
• 1 3 3 1
• 1 4 6 4 1
• 1 5 10 10 5 1

• 0= event never occurs
• 1= event always occurs

• -heads tails
• -HH TT HT TH
• -1 2 3 4 5 6

Prob.= (# of successful outcomes)÷(# of total outcomes)

• opposite of event
• 1-fraction probability= compliment

2 events that can't occur at the same time, only use the word OR with this condition

add two conditions and subtract overlap

• Example:
• P(king) + P(club) - P(king of clubs)
• 4/52 + 13/52 - 1/52

if event A doesn't affects the probability of event B

P(A AND B)= P(A) • P(B)

Don't forget to reduce the denominator by one for each next fraction because you wouldn't be returning "the marbles to the bag"

REWRITE THE QUESTION. Find out what you need and write out what you're finding the probability for.

Example: P(1st yes AND 2nd yes AND 3rd yes)

conditional statement using the words "if" or "given that"

P(B given A)= P(A and B) ÷ P(A)