Questions: Five study Questions EQ: What is probability and how does it help explain the results of genetic crosses? Probability and Heredity In football they use the coin toss to determine who kicks and receives the ball at the beginning of a game. What is the likelihood of a team winning the coin toss can be determined by probability. Probability Principles of Probability : is a number that describes how likely it is for a certain event to occur. Mathematics of Probability Ex: Coin toss can land either heads or tails (it can only land in two possible ways) These two events are equally likely to occur, so in mathematical terms, you can say a coin has a probability of 1 in 2 chances to land on heads, same with tails (1 in 2 probability) Probability can be expressed three ways: Ratio Fraction Percentage 1:2 ½ 50% Math Skills: Percentage A percentage (%) is a number compared to 100. Ex: 50% means 50 out of 100 Suppose you toss a coin 5 times and the coin landed on heads 3 times out of 5 tosses. Here s how you can calculate what percent the coin landed on heads.
Steps to calculating percentage 1. Write the comparison as a fraction. 3 out of 5 = 3/5 2. Setup the equation by multiplying the fraction by 100% to express the probability as a percentage 3/5 x 100% = 3. Divide the top number of the fraction by the bottom number 3 5=.6 4. Multiply the decimal by 100%.6 x 100%= 60% The laws of probability predict what is likely going to occur, not what will occur! Ex: If you throw a coin 20 times, you would expect it to land on heads 10 times because it has a probability of 1 in 2, but instead is lands on heads 11 times. The more times you toss the coin the closer the actual results will be to the results predicted by probability. Independence of Events The result of one coin toss does not affect the outcome of the next coin toss. They are separate events and the results are independent of each other. Ex: A coin lands on heads five times in a row doesn t mean the 6 th toss will result in the coin landing on heads. There is still a 1 in 2 chance for the coin to land on heads because each throwing event is independent from each other.
Probability and Genetics How is probability related to genetics? When Mendel crossed two hybrid plants (Tt) for height, ¾ of the F 1 plants had tall stems and ¼ of the plants had short stems These results repeated and Mendel realized that probability is related to his work. The plants have a 3 in 4 chance of having a long stem and 1 in 4 chance to have a short stem Mendel was the first to discover that the principles of probability can be used to determine genetic crosses Punnett Squares Punnett Squares : a chart that shows all the possible combinations of alleles that can result from a genetic cross Geneticists use Punnett Squares to determine all the possible outcomes of a genetic cross. How to make a Punnett Square 1. Draw a box and divide into 4 squares 2. Write the male s alleles at the top of the box and the female s alleles along the left side of the box
3. Copy the Female Parent s Alleles into the boxes (to the right of them) 4. Copy the Male Parent s Alleles into the boxes (beneath them) 5. The completed Punnett Square shows all the possible allele combinations in the offspring.
Using a Punnett Square In a genetic cross, the allele that each parent will pass on to its offspring is based on probability. RR = 1 in 4 or 25% rr = 1 in 4 or 25% Rr = 2 in 4 or 50% RR and Rr alleles create round seeds, while rr alleles create wrinkle seeds The probability of offspring seeds being round is 3 in 4 (75%) {Remember the Uppercase R is dominant for round seeds} and the probability of offspring seeds being wrinkled are 1 in 4 (25%). Predicting Probabilities You can use a Punnett Square to predict probabilities Ex: Crossing a purebred black furred guinea pig with a purebred white furred guinea pig Bb= 4 in 4 (100%) chance the guinea pig will have black fur