Odds in favor
odds in favor of events occurring given by a ratio of probability
odds in favor of A: A= probability of A / probability that A wont happen A = P(A)/P(A’)
Example problem
Drawer contains 3 red socks, 5 white socks and 4 black socks What is the odds that they grab red socks?
P(redsocks) = 3/12 = 0.25 P(redsocks’) = 0.75 A = 0.25:0.75 = 1/3
Can also be done very simply with just counting. # red socks / # non red socks 3 / 9 = 1/3
Odds against
odds against A = Probability against A / Probability of A against A = P(A’)/P(A)
Odds in favor and Odds against are reciprocals. if you know one, you know the other.
Colon notation
Same thing as the division, just different notation. 4/6 same as 4:6
Probability from Odds
just know that odds for + odds against = total permutations
P(A) = odds(A)/odds(A)+odds(A’) P(A’) = odds(A’)/odds(A)+odds(A’)
odds in favor: h/k will have a probability of h/h+k same deal for odds against