How to Calculate the Probability of a Punnett Square

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In the 1800s, Gregor Mendel predicted how genes worked to pass on physical traits to offspring and calculated the probabilities of certain traits being inherited. Though scientists did not even discover the existence of genes until later, Mendel's basic principles proved correct. Reginald Punnett developed the Punnett square as a graphical method to calculate the probability of inheritance based on Mendel's principles. You do not have to understand statistics and probability to calculate with a Punnett square; just create the square and observe the results to determine the probability of an offspring inheriting a certain trait.

    Draw a square and divide it into four smaller squares with one horizontal and one vertical line.

    Write the genotype of one parent above the square, using a capital letter for the dominant allele and a lowercase letter for the recessive allele. Write one allele above the left box and the other allele over the right box. Consider the example of a Punnett square for eye color with brown eyes being dominant and blue eyes being recessive. If the parent has a genotype with one dominant and one recessive allele, write "B" above one box for the dominant allele and "b" above the other box for the recessive allele.

    Write the genotype of the other parent to the left of the square. Put one allele to the left of the top box and the other allele to the left of the bottom box. If the genotype has two recessive alleles, for example, write "b" next to each box.

    Fill in each box with the alleles written above and to the left of it. If the upper left box has "B" above and "b" to the left, for example, write "Bb" in the box. If the upper right box has "b" above and "b" to the left, write "bb" in the box. Do the same for the two bottom boxes.

    Count the number of boxes containing at least one dominant allele. In the case of one parent with the genotype Bb and one parent with the genotype bb, the boxes contain Bb, bb, Bb and bb. Two of the boxes in this case have a dominant allele.

    Divide the number of boxes with a dominant allele by four and multiply the result by 100 to get the percent chance that an offspring will have the dominant trait. For example (2/4)*100 = 50, so there is a 50 percent chance of an offspring having brown eyes.

    Subtract the percent chance for the dominant trait from 100 to get the percent chance that an offspring will display the recessive trait. For example, 100 - 50 = 50, so there is a 50 percent chance of an offspring having blue eyes.

    Tips

    • Realize that probabilities do not guarantee a certain outcome. If the Punnett square predicts 50 percent blue eyes and 50 percent brown eyes, for example, the parents could end up having 40 percent children with blue eyes and 60 percent with brown eyes, or even children who all have the same color eyes.

References

About the Author

Petra Wakefield is a writing professional whose work appears on various websites, focusing primarily on topics about science, fitness and outdoor activities. She holds a Master of Science in agricultural engineering from Texas A&M University.

Photo Credits

  • Jack Hollingsworth/Photodisc/Getty Images

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