(Read 3.1 to get acquainted with casino games.)
Experiment: a process by which an outcome is obtained, i.e., rolling a die. Sample space: The set S of all possible outcomes of an experiment. i.e. the sample space for a die roll is {1, 2, 3, 4, 5, 6} Event: Any subset E of the sample space. i.e. Let E E
The If an experiment’s outcomes are equally likely to occur, then the probability of an event E is the number of outcomes in E divided by the number of outcomes in the Sample Space. P(E) = n(E)/n(S) This chapter only discusses experiments with equally likely outcomes. Note: Probability
=
O(E) = n(E) : n(E’) Odds = (success) : (failure) House odds vs. True odds What the casino pays vs. what you should get
On a Roulette wheel, find: a) the probability of getting a red number b) the odds of getting a red number c) the probability of getting number 20 d) the odds of getting number 20 e) the probability of getting a number between 1 and 12 inclusive f) the odds of getting a number between 1 and 12 inclusive a) 18/38 = 9/19 b) 18: 20 = 9: 10 c) 1/38 d) 1: 37 e) 12/38 = 6/19 f ) 12 : 26 = 6 : 13 Probability can be found
If we flip a coin and record how many heads comes up, then it is called relative frequency of heads. The results may not be exactly the ½ probability that theory provides, but if the coin is flipped a large number of times, the relative frequency will come close to the ½ probability. This is called the Law of Large Numbers. Gregor Mendel’s experiments in genetics first used
probability. Genes are recessive
and dominant. Using pea plants, he
studied the outcome of cross-pollinating red and white flower plants.
At the time, predictions were that the flowers would turn out pink.
He made sure the flowers were pure color, 1 Using a Punnett Square: R, R R = red, w = white w ( R, w) (R, w) Results were all Red Flowers w ( R, w) (R, w) For the 2 Thus Red was dominant and white recessive. R w Results: 3 Red, 1 white flower. R (R, R) (R, w) w (R, w) (w, w) Third generation: One true Red, 2 red with white carriers, 1 true white. Applications of probability in genetics include predictions, likelihoods of passing genetic material to offspring. Decisions can be made whether to have children if a person is a carrier of a fatal disease. Huntington’s disease is caused by a dominant gene. Woody Guthrie, famous folksinger-song-writer died of the disease at age 55. His son Arlo Guthrie did not want to be tested for the disease, there is no cure. Sickle-cell anemia is another disease, less fatal, but dangerous.
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