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So why did Mendel repeatedly obtain 3:1 ratios in his crosses? To understand how Mendel deduced the basic mechanisms of inheritance that lead to such ratios, we must first review the laws of probability.

Probability basics

Probabilities are mathematical measures of likelihood. The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of opportunities for the event to occur. It is also possible to calculate theoretical probabilities by dividing the number of times that an event is expected to occur by the number of times that it could occur. Empirical probabilities come from observations, like those of Mendel. Theoretical probabilities come from knowing how the events are produced and assuming that the probabilities of individual outcomes are equal. A probability of one for some event indicates that it is guaranteed to occur, whereas a probability of zero indicates that it is guaranteed not to occur. An example of a genetic event is a round seed produced by a pea plant. In his experiment, Mendel demonstrated that the probability of the event “round seed” occurring was one in the F 1 offspring of true-breeding parents, one of which has round seeds and one of which has wrinkled seeds. When the F 1 plants were subsequently self-crossed, the probability of any given F 2 offspring having round seeds was now three out of four. In other words, in a large population of F 2 offspring chosen at random, 75 percent were expected to have round seeds, whereas 25 percent were expected to have wrinkled seeds. Using large numbers of crosses, Mendel was able to calculate probabilities and use these to predict the outcomes of other crosses.

The product rule and sum rule

Mendel demonstrated that the pea-plant characteristics he studied were transmitted as discrete units from parent to offspring. As will be discussed, Mendel also determined that different characteristics, like seed color and seed texture, were transmitted independently of one another and could be considered in separate probability analyses. For instance, performing a cross between a plant with green, wrinkled seeds and a plant with yellow, round seeds still produced offspring that had a 3:1 ratio of green:yellow seeds (ignoring seed texture) and a 3:1 ratio of round:wrinkled seeds (ignoring seed color). The characteristics of color and texture did not influence each other.

The product rule    of probability can be applied to this phenomenon of the independent transmission of characteristics. The product rule states that the probability of two independent events occurring together can be calculated by multiplying the individual probabilities of each event occurring alone. To demonstrate the product rule, imagine that you are rolling a six-sided die (D) and flipping a penny (P) at the same time. The die may roll any number from 1–6 (D # ), whereas the penny may turn up heads (P H ) or tails (P T ). The outcome of rolling the die has no effect on the outcome of flipping the penny and vice versa. There are 12 possible outcomes of this action ( [link] ), and each event is expected to occur with equal probability.

Questions & Answers

effect of planning beans of using fertilizer
Elizerbeth Reply
what do we mean by transgenic organisms?
FADILAT Reply
what is or are the functions of the Islets of Langarhaans
FADILAT
They are the regions of the pancreas that contains the endocrine cell
Iyadi
is the studly of life
Aisha Reply
what is biology
Asunta Reply
is the study of living organism and their interection with one another and their environment.
Belbon
what is soil
Mukisa Reply
the top layer of the earth in which plant's, tree's
Ahmad
type of soil
Asunta
function of cell wall
Nthati Reply
function of cell wall
Asunta
To protect the cell from bursting
Maurice
to protect the cell from bursting
Deborah
to protect all other internal components of the cell
Olaoye
What is escherichia coli
Tumise Reply
in what type of cells is meiosis taking place?
Rhyeann Reply
sex cells
Eric
hlo
Amit
reproductive system of earthworm plzz describes
Amit
procryotic cell and some eucaryotic cell
Olaoye
applications of biology
Namawejje Reply
what is dormancy?
Aliyu Reply
hello guys what's the difference between prokaryotes and eukaryotes
Nwachukwu Reply
hlo what are the applications of biology?
Namawejje
eukaryotic cells have DNA in their nucleus while prokaryotic cells have their DNA present freely in their cytoplasm.
FADILAT
deviation from mendelian
Ogali Reply
what is lethal allele
Ogali
Explain how chemical , bioligical and physical interaction between themselves and the non living components ?
Beyan Reply
what is Tissues
Faith Reply
Group of similar cells performing some related functions We have some type of tissues Connective Muscle Epithelial Nervous tissues
peter
group of cells that is called tissue.
Nikita
tissue is the arrangement or combination of similar cells that perform the same function .
FADILAT
what is abiotic?
Williams Reply
state 2 abiotic factors that affect the rate of transpiration in plants?
Benenge
non living things
Chris
1) temperature:the temperature of the atmosphere affects the opening and closing of the stomata in the leaves of plants .high temperature encourages water loss . 2)wind : air flow encourages transpiration in plants . example,plants that are found on high areas like mountains transpire easily
FADILAT
I agree with Fadilat Muhammad In addition, water plants tend to reserve water during dry seasons so if they are not given plenty of water, they keep the water to them selves
Iyadi

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Source:  OpenStax, Biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11448/1.10
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