PROBABILITY

1/7/96, 5 Jan 00, 7 Jan 05

Tamarin, p64-67, GMSLG 5^th: p 30-31, GMSLG 7^th: 37-38, 8^th: 94-99

Mendel was successful in part because he could fit inexact numbers to ratios following the rules of probability

Random (stochastic) events cause variation in the outcome of the H or T of a flip.

probability of an event = # favorable cases/# total cases

             six sided di,                                 rolling a 1 has probability of 1/6

             7 clubs out of a deck = 1/52        any spade = 13/52

event with certainty has probability of 1/1 = 1

probability of an event A and probability of a non-A event = 1

PRODUCT RULE (THE AND RULE)

Probability of the occurrence of two ore more independent events is the product of their probabilities:

                   What is the chance of rolling a one and then a six?                              [= 1/6 x 1/6 = 1/36] 

                   Snake eyes?                                                                                           [= 1/6 x 1/6 = 1/36]

                   What is the chance of rain both today (50%) and tomorrow(20%)?     [= 0.5 x 0.1 = 0.05]

                   What is prob of getting aabbcc from AaBbCc times self?                    [= (½ x ½ x ½)²]

SUM RULE (THE EITHER/OR RULE)

Probability of any one of several mutually exclusive events occurring is equal to the sum of their individual probabilities:

                          What is the chance of rolling a 1 or a 6 with a di?                          [= 1/6 + 1/6 = 2/6]

                          What is chance of drawing any face card?                                      [=1/13 + 1/13 + 1/13 = 3/13]

harder:              What is chance or rain either today (50%) or tomorrow (20%)?    [= (1-0.5) x (1-0.2)= 0.4]

What is the probability a brown eyed man who has 4 brown eyed children with a blue eyed woman is heterozygous? What is the probability that he is homozygous?

             Assume he is heterozygous, calculate probability of each child being brown eyed, multiply all

[=1-(½*½*½*½) = 15/16]

BINOMIAL THEOREM:

             Probability of the occurance of events with unspecified order is defined by binomial theorem

what is prob of tossing two pennies and getting a H and a T?

P = (n!/s!t!) x p^sq^t                       n = number of trials

                                                    s = number of times X happens

                                                    t = number of times Y occurs (X does not happen)

                                                    p = probability that X will occur

                                                    q = probability that Y occurs

what is the probability that a family with 6 children has 5 boys and one girl?

P = (n!/s!t!) x p^sq^t = (6!/(5! x 1!)) x (1/2)⁵ (1/2)¹ 

                          = 6(1/2)⁶ = 6/64