Principles of Probability Probability – a number that describes how likely it is that an event will occur Mathematics of probability – In a coin toss there are 2 possible outcomes. The coin can land heads up or tails up. Each result has an equal chance of occurring – 1 out of 2. Probability can be expressed as a ratio, fraction orpercent – 1:2, ½, or 50%
Percentage• Percentage – a number compared to 100• If 3 out of 5 coins land with heads up. The percentage is calculated as follows: l 3 out of 5 = 3/5 3/5 x 100% = 60%• Practice: Suppose 3 out of 12 coins landed with tails up. How can you express this as a percentage?
Percentage 3 out of 12 = 3/12 or ¼ ¼ x 100% = 25% 1
Independence of Events The results of one coin toss do not affect the results of subsequent coin tosses Each event occurs independently Ex. If you toss a coin 5 times and it lands heads up each time. What is the probability that it will land heads up on the next toss?
Independence of Events The probability is still 1 out of 2 or 50%
Probability and Genetics• Mendel was the first to recognize that the principles of probability could be used to predict the results of genetic crosses• When he crossed the two plants that were hybrids for stem height, ¾ had tall stems and ¼ had short stems• The probability of such a cross producing tall stems was 3 in 4. The probability of producing short stems was 1 in 4
Punnett Squares A chart that shows all the possible combinations of alleles that can result from a genetic cross
To make a Punnett square• 1. draw a box and divide it into 4 boxes• 2. Write male parent’s alleles along the top and female parent’s alleles along the side R r R r
Punnett Square3. Copy the female parent’s alleles into the boxes to their right R r R R R R r r r4. Copy the male parent’s alleles into the boxes beneath them R r R RR Rr r Rr rr
Using a Punnett Square The Punnett square show all the possible allele combinations in the offspring In a genetic cross the allele that a parent passes on to an offspring is based on probability
Predicting Probabilities Punnett squares can be used to predict probabilities. If a purebred pink flamingo is crossed with a purebred blue flamingo. There is a 100% probability that the offspring will be pink
Phenotypes and Genotypes Phenotype – an organism’s physical appearance, or visible traits (what you see) Genotype – genetic makeup, or allele combination The genotypes Tt and TT have the same phenotype – tall The genotype tt has the phenotype short
Phenotypes and Genotypes Homozygous- an organism that has two identical alleles for a trait Ex. TT or tt Heterozygous – an organism that has two different alleles for a trait. Also called hybrid Ex.Tt
Codominance Not all traits have alleles that are dominant or recessive. Codominance – both alleles are expressed in the offspring
Examples of codominance ABO blood types Fur color in mammals Spotted flowers