<p> PROBABILITY AND GENETICS</p><p>Probability: is the chance or likelihood of a particular outcome (event) expressed as a ratio.</p><p>A probability will have a range between 0 -1.</p><p>The sum of the probabilities must add up to 1.</p><p>Example:</p><p>Using a two headed coin, a) what is the probability of tossing heads? 1</p><p> b) what is the probability of tossing tails? 0</p><p> c) what is the sum of the probabilities? 1 + 0 = 1</p><p>Using a two headed coin a) what is the probability of tossing heads? 1/2</p><p> b) what is the probability of tossing tails? 1/2</p><p> c) what is the sum of the probabilities? 1/2 + 1/2 = 1</p><p>Using a deck of cards a) what is the probability of drawing the queen of hearts? 1/52</p><p> b) what is the probability of drawing any other card? 51/52</p><p> c) what is the sum of the probabilities? 1</p><p>Using a die a) what is the probability of rolling a 3? 1/6</p><p> b) what is the probability of rolling a 6? 1/6</p><p> c) what is the probability of rolling any other number? 4/6</p><p> d) what is the sum of the probabilities? 1</p><p>In tossing a coin, what ever happened during the first toss is independent of the outcome of the second toss.</p><p>Therefore successive coin tosses are independent events.</p><p>In a series of five tosses, five heads were obtained. What is the possibility that the sixth toss will be heads? be tails?</p><p>When working with probabilities there are two basic laws of probability that can be used when solving genetic problems; </p><p> a) RULE OF MULTIPLICATION and </p><p> b) RULE OF ADDITION. RULE OF MULTIPLICATION</p><p>Take two coins are toss at the same time. Remember that each toss is independent of the other.</p><p>What is the probability that both coins will turn up heads? ______</p><p>In order to determine this probability you must</p><p> i) calculate the probability of each independent event</p><p> ii) multiply each individual probability to obtain an overall probability of these events occurring in combination.</p><p>Fraction Percent</p><p>What is the probability that the first coin will be heads? 1/2 50%</p><p>What is the probability that the second coin will be heads? 1/2 50 %</p><p>What is the probability that BOTH coins will be heads? 1/2 x 1/2 = 1/4 25%</p><p>The concept of a coin toss is similar to the events that would take place in a monohybrid cross.</p><p>Example: In flower colour a red (R) flower is dominant to a white (r) flower. If both parents are heterozygous red (Rr), What is the probability that they would produce a white flower?</p><p>Remember the law of segregation states that like alleles must segregate (separate) from each other.</p><p>Phenotype Red Red</p><p>Genotype Rr Rr</p><p> segregation segregation of alleles of alleles</p><p>Gamete 1/2 R 1/2 r 1/2 R 1/2 r</p><p>What is the probability of two recessive (r) alleles coming together at fertilization? (Hint probability of two heads)</p><p>Each event is independent of each other. In the male plant half (1/2) the gametes will contain the recessive allele r. The same is true for the female plant in that half (1/2) the gametes will contain the recessive allele r. The probability that both of these alleles will come together is the product of each independent event.</p><p>1/2 x 1/2 = 1/4 (similar to tossing two coins and both coins turning up heads)</p><p>There is a 25% chance that a white flowered offspring will be produced. THE RULE OF ADDITION</p><p>Rule of Addition: the probability of an event that can occur in two or more different ways is the sum of the separate probabilities of those ways.</p><p>Example: Assume both plants are heterozygous red (Rr). What is the probability that they would produce an offspring that is heterozygous red (Rr)?</p><p>Phenotype Red Red Genotype Rr Rr</p><p> segregation segregation of alleles of alleles</p><p>Gamete 1/2 R 1/2 r 1/2 R 1/2 r</p><p>There are two possible events that could take place.</p><p> a) the dominant allele comes from the egg and the recessive allele comes from the pollen.</p><p>Probability = 1/2 R (egg) x 1/2 r (pollen) = 1/4 Rr</p><p> b) the dominant allele comes from the pollen and the recessive allele comes from the egg.</p><p>Probability = 1/2 R (pollen) x 1/2 r (egg) = 1/4 Rr</p><p>Because these are two possible events that could take place, the probability is the sum of the two separate events</p><p>1/4 + 1/4 = 2/4</p><p>There is a 50% chance that a heterozygous red plant would be produced.</p><p>These probabilities can be easily calculated by using a punnet square.</p><p>Example: Two heterozygous red plants are cross-pollinated, determine the probability of producing red and white offspring's.</p><p>Egg 1/2 R 1/2 r Probability of each Pollen independent event</p><p>1/2 R 1/4 RR 1/4 Rr</p><p>Probability of each Probability of these event independent event occurring in combination. 1/2 r 1/4 Rr 1/4 rr</p><p>Probability of having a Genotype Probability Fraction Percentage Ratio</p><p> homozygous red is RR 1/2 R x 1/2 R 1/4 25% 1 heterozygous red is Rr 1/2R x 1/2r 1/4 1/4 + 1/4 =1/2 50% 2 heterozygous red is Rr 1/2r x 1/2R 1/4 homozygous white is rr 1/2 r x 1/2 r 1/4 25% 1 PROBABILITY AND GENETICS</p><p>Probability: ______</p><p>A probability will have a ______.</p><p>The ______of the probabilities must ______.</p><p>Example:</p><p>Using a two headed coin, a) what is the probability of tossing heads? ______</p><p> b) what is the probability of tossing tails? ______</p><p> c) what is the sum of the probabilities? ______</p><p>Using a two headed coin a) what is the probability of tossing heads? ______</p><p> b) what is the probability of tossing tails? ______</p><p> c) what is the sum of the probabilities? ______</p><p>Using a deck of cards a) what is the probability of drawing the queen of hearts? ______</p><p> b) what is the probability of drawing any other card? ______</p><p> c) what is the sum of the probabilities? ______</p><p>Using a die a) what is the probability of rolling a 3? ______</p><p> b) what is the probability of rolling a 6? ______</p><p> c) what is the probability of rolling any other number? ______</p><p> d) what is the sum of the probabilities? ______</p><p>In tossing a coin, what ever happened during the first toss is ______of the outcome of the second toss.</p><p>Therefore successive coin tosses are independent events.</p><p>In a series of five tosses, five heads were obtained. What is the possibility that the sixth toss will be heads? be tails?</p><p>When working with probabilities there are two basic laws of probability that can be used when solving genetic problems; </p><p> a) ______and </p><p> b) ______RULE OF MULTIPLICATION</p><p>Take two coins are toss at the same time. Remember that each toss is independent of the other.</p><p>What is the probability that both coins will turn up heads? ______</p><p>In order to determine this probability you must</p><p> i) ______</p><p> ii) ______</p><p>______</p><p>Fraction Percent</p><p>What is the probability that the first coin will be heads?</p><p>What is the probability that the second coin will be heads?</p><p>What is the probability that BOTH coins will be heads?</p><p>The concept of a coin toss is similar to the events that would take place in a ______.</p><p>Example: In flower colour a red (R) flower is dominant to a white (r) flower. If both parents are heterozygous red (Rr), What is the probability that they would produce a white flower?</p><p>Remember the law of segregation states that like alleles must segregate (separate) from each other.</p><p>Phenotype</p><p>Genotype</p><p> segregation segregation of alleles of alleles</p><p>Gamete</p><p>What is the probability of two recessive (r) alleles coming together at fertilization? (Hint probability of two heads)</p><p>Each event is independent of each other. In the ______the gametes will contain the recessive allele r. The same is true for the ______the gametes will contain the recessive allele r. The probability that both of these alleles will come together is the ______. THE RULE OF ADDITION</p><p>Rule of Addition: the probability of an event that can occur in ______is the ______of the ______of those ways.</p><p>Example: Assume both plants are heterozygous red (Rr). What is the probability that they would produce an offspring that is heterozygous red (Rr)?</p><p>Phenotype Red Red Genotype Rr Rr</p><p> segregation segregation of alleles of alleles</p><p>Gamete 1/2 R 1/2 r 1/2 R 1/2 r</p><p>There are two possible events that could take place.</p><p> a) the dominant allele comes from the egg and the recessive allele comes from the pollen.</p><p> b) the dominant allele comes from the pollen and the recessive allele comes from the egg.</p><p>Because these are two possible events that could take place, the probability is the sum of the two separate events</p><p>These probabilities can be easily calculated by using a ______-.</p><p>Example: Two heterozygous red plants are cross-pollinated, determine the probability of producing red and white offspring's.</p><p>Egg 1/2 R 1/2 r Probability of each Pollen independent event</p><p>1/2 R</p><p>Probability of each independent event 1/2 r</p><p>Probability of having a Genotype Probability Fraction Percentage Ratio</p><p> homozygous red is</p><p> heterozygous red is</p><p> heterozygous red is</p><p> homozygous white is</p>