Probability & Genetics Drawing from the Deck of Genes Probability & Genetics

# of all possible outcomes PROBABILITY Likelihood that a specific event will occur Can be determined by a formula: Probability = # of one kind of possible outcome total # of all possible outcomes

Predicting a chance event Use probability to figure out your chances of pulling cards out of a deck. Predict possibility of genetic traits appearing in offspring

1,3,5 3/6 = 1/2 What is the probability of a coin landing heads up? What is the probability of a coin landing tails up? 3. You have a deck of cards ( 52 cards). What is the probability of picking two red queens? 2/52 X 2/52 = 4. A die has six sides. What is the probability of rolling an odd number? 1,3,5 3/6 = 1/2

FIRST LAW OF PROBABILITY Probability has NO MEMORY 6. If you toss a coin 100 times, what is the probability it will land on heads? 1/2 7. You have tossed a coin 10 times and each time it has landed on heads, what is the probability the next toss will land tails up? 1/2

FIRST LAW OF PROBABILITY “The outcome (result) of a chance event is never influenced by previous results.” EXAMPLE: Chances of have a boy? After having 3 or 4 girls, what are the chances for a boy ? 1/2 still 1/2

Second Law of Probability: PRODUCT RULE “Probability of 2 chance events occurring together is the MULTIPLICATION PRODUCT of the individual probabilities.” 8. What is the probability of tossing two heads in a row? ½ x ½ = 9. What is the probability of tossing four heads in a row? ½ x ½ x½ x ½ =

PUNNETT SQUARES Can be used to PREDICT Important in Genetics because: Used to predict FREQUENCY Of gametes and offspring Valid only when LARGE NUMBERS are used gametes

Genetics & Probability Mendel’s Laws: Segregation Independent assortment Reflect same laws of probability that apply to tossing coins or rolling dice

Second Law of Probability The rule of multiplication To find the probability of 2 chance events occurring together Multiply product of their separate probabilities ½ B X ½ b = ¼ Bb F1 Genotypes B b female B b male Formation of eggs Formation of sperm 1/2 B B 1/2 1/2 B B b b 1/4 1/2 (1/2  1/2) b B B b 1/4 1/4 b b F2 Genotypes 1/4 Figure 9.13

2nd Law of Probability Ex: If your chances of pulling an ace from a deck of cards is 4/52 (1/13) and Your chances of pulling a heart is 13/52 (1/4) , then your chance of getting an ace of hearts is: 1/13 x ¼ = 1/52