Probability and Punnett Squares

Tossing Coins

• If you toss a coin, what is the probability of getting heads? Tails? If you toss a coin 10 times, how many heads and how many tails would you expect to get? Working with a partner, have one person toss a coin ten times while the other person tallies the results on a sheet of paper. Then, switch tasks to produce a separate tally of the second set of 10 tosses.

Tossing Coins (continued)

• 1. Assuming that you expect 5 heads and 5 tails in 10 tosses, how do the results of your tosses compare? How about the results of your partner’s tosses? How close was each set of results to what was expected?

• 2. Add your results to those of your partner to produce a total of 20 tosses. Assuming that you expect 10 heads and 10 tails in 20 tosses, how close are these results to what was expected?

• 3. If you compiled the results for the whole class, what results would you expect?

• 4. How do the expected results differ from the observed results?

Probability

Likelihood that a particular event will occur is called probability

Ex. Coin tossing – probability that a coin will land heads up is 1 chance in 2 tries = ½ or 50% chance

Toss the coin 3 times, probability of each coin landing heads up is ½ for each of the three tosses:

½ x ½ x ½ = 1/8 (flip 1) (flip 2) (flip 3) = 1/8

1/8 chance of flipping heads 3 times in row

Probability (continued)

• Past outcomes do not affect future ones. Alleles separate completely random, like a coin flip. The Principles of Probability can be used to predict the outcomes of genetic crosses.

Punnett Squares

• Gene combinations that might result from a genetic cross can be determined by diagrams called Punnett Squares. Parents’ alleles are placed along the top and sides of the squares while the offsprings’ alleles are inside the squares. Capital letters = dominant allele while lowercase letters = recessive alleles

Punnett Squares

“T” = tall plant

“t” = short plant

Punnett Squares

“T” = tall plant

“t” = short plant

Punnett Squares (continued)

• Two identical alleles for a trait (TT or tt) = homozygous (true-breeding)

• Two different alleles for a trait (Tt) = heterozygous (hybrids)

• Phenotype = physical, observable characteristics

• Genotype = genetic make-up, NOT observable

Probability and Segregation“T” = tall plant

“t” = short plant

Genotype Ratio: 1 TT : 2 Tt : 1 tt

•1/4th of F2 plants have TT

•½ of F2 plants have Tt

•1/4th of F2 plants have tt

Phenotype Ratio: 3 Tall : 1 Short

•3 Tall plants (1 TT, 2 Tt) for every 1 short plant (1 tt)

•Ratio of 3 : 1 for tall to short plants

Probabilities Predict Averages

– Probability cannot predict precise outcomes, but is usually close

– The larger the sample size of offspring, the closer the observed data will be to the expected data

Setting Up Punnett SquaresCross a Homozygous Yellow Seed Plant ( YY) with

a Heterozygous Yellow Seed Plant (Yy)

YY x Yy

Y = yellow seed

y = green seed

Y Y

Y

y

Y Y

Y Y

Genotype Ratio:

2 YY : 2 Yy

Reduces to

1 YY : 1 Yy

Phenotype Ratio:

All yellow seeds

100 % yellow seeds

Y Y

y y

yellow yellow

yellow yellow