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Inheritance and Probability

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Mendelian inheritance reflects rules of probability Mendel’s Laws of Segregation and Independent Assortment reflect the same laws of probability that apply to tossing coins or rolling dice. The probability scale ranged from zero (an event with no chance of occurring) to one (an event that is certain to occur).

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Tossing a coin/Rolling a die The probability of tossing heads on a coin is 1/2. The probability of rolling a 3 with a six-sided die is 1/6. The probability of rolling any other number is 1 - 1/6 = 5/6.

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When tossing a coin, the outcome of one toss has no impact on the outcome of the next toss. Each toss is an independent event, just like the distribution of alleles into gametes. –Like a coin toss, each ovum from a heterozygous parent has a 1/2 chance of carrying the dominant allele and a 1/2 chance of carrying the recessive allele. –The same odds apply to the sperm.

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Rule of Multiplication AKA Product Law When to use it: –When you want to determine the probability that two or more independent events will occur together is equal to their individual probability of occurrence. How to use it: –Compute the probability of each independent event. –Then, multiply the individual probabilities to obtain the overall probability of these events occurring together.

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EXAMPLES –The probability that two coins tossed at the same time will land heads up is 1/2 x 1/2 = 1/4. –Similarly, the probability that two heterogyzous pea plants (Pp) will produce a white-flowered offspring depends on an ovum with a white allele mating with a sperm with a white allele. 1/2 x 1/2 = 1/4.

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The Rule of Multiplication can apply to dihybrid crosses. –We can use this to predict the probability of a particular F 2 (YyRr) plant having yellow and round seeds, without constructing a 16-part Punnett square. ¾ plants should be YY or Yy to get yellow ¾ plants should be RR or Rr to get round ¾ x ¾ = 9/16 Proof on next slide

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Proof YRYryRyr YRYYRRYYRrYyRRYyRr YrYYRrYyrrYyRrYyrr yRYyRRYyRryyRRyyRr yrYyRrYyrryyRryyrr

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Rule of Addition AKA Sum Law The Rule of Addition also applies to genetic problems. Under the Sum Law, the probability of an event that can occur two or more different ways is the sum of the individual events.

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–For example, there are two ways that F 1 gametes can combine to form a heterozygote. The dominant allele could come from the sperm and the recessive from the ovum (probability = 1/4). Or, the dominant allele could come from the ovum and the recessive from the sperm (probability = 1/4). The probability of a heterozygote is 1/4 + 1/4 = 1/2.

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Warm-Up 1. What is the phenotypic ratio and genotypic ratio of the offspring of a monohybrid cross? 2. What is the phenotypic ratio of a dihybrid cross?

Warm-Up 1. What is the phenotypic ratio and genotypic ratio of the offspring of a monohybrid cross? 2. What is the phenotypic ratio of a dihybrid cross?

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