Drawing from the Deck of Genes Probability & Genetics.

Drawing from the Deck of GenesDrawing from the Deck of Genes

Probability & Genetics

PROBABILITY• Likelihood that a specific event will occur

• Can be determined by a formula:

ProbabilityProbability = # of one kind of possible outcome total# of one kind of possible outcome total

# of all possible outcomes # of all possible outcomes

Predicting a chance eventPredicting 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. What is the probability of a coin landing heads up?

1/2

2. What is the probability of a coin landing tails up?

1/2

3/6 = 1/2

3. You have a deck of cards ( 52 cards). What is the

probability of picking two red queens?

2/52 X 2/52 =2/52 X 2/52 =4. A die has six sides. What is the probability of rolling an odd number?

1,3,5

FIRST LAW OF PROBABILITY

• Probability has NO MEMORY

6. If you toss a coin 100 times100 times, what is the probability it will land on heads?heads?

7. You have tossed a coin 10 times10 times and each time it has landed on heads, what is the probability the next toss will land tails tails up?

1/21/2

1/21/2

FIRST LAW OF PROBABILITYFIRST LAW OF PROBABILITY

• “The outcome (result) of a chance event is never influenced by previous results.”

• EXAMPLE:EXAMPLE:

• Chances of have a boy?Chances of have a boy?

• After having 3 or 4 girls, After having 3 or 4 girls, what are the chances for a what are the chances for a boy ?boy ?

1/21/2

still 1/2still 1/2

Second Law of Probability: PRODUCT RULESecond Law of Probability: PRODUCT RULE

• “Probability of 2 chance events occurring together is

the MULTIPLICATION PRODUCTMULTIPLICATION PRODUCT of the individual probabilities.”

8. What is the probability of tossing two headstwo heads in a row?

½ x ½ =½ x ½ =

9. What is the probability of tossing four headsfour heads in a row?

½ x ½ x½ x ½ =½ x ½ x½ x ½ =

PUNNETT SQUARES

• Can be used to PREDICT

Important in Genetics because:Important in Genetics because:

Used to predict FREQUENCY Of gametes and offspring

Valid only when LARGE NUMBERS are used

gametesgametes

Genetics & Probability

• Mendel’s Laws:

Segregation

Independent assortment

Reflect same laws of probability that apply to tossing coins or rolling dice

• The rule of The rule of multiplicationmultiplication

• To find the probability of 2 chance events occurring together

• Multiply product of their separate probabilities

• ½ B X ½ b = ¼ Bb

Second Law of Probability

Figure 9.13

F1 Genotypes

B b female B b male

Formation of eggs Formation of sperm

1/2

B B

1/2

b

1/2B B

1/4

(1/2 1/2)

1/2

b

b B

1/4

B b

1/4

b b

1/4F2 Genotypes

22ndnd Law of Probability Law of Probability

• Ex: If your chances of pulling an ace ace from a deck of cards is 4/52 (1/13)4/52 (1/13) and

• Your chances of pulling a heartheart is 13/52 (1/4)13/52 (1/4) , then your chance of getting an ace of hearts is:

• 1/13 x ¼ = 1/52