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Q46 - Mendelian Probability in Pea Pods

Theoretical 2 Real exam question - full text reproduced under IBO's CC BY-NC-SA 4.0 license
Mendel's Laws & Probability in Genetics

A green and wrinkled seeds pea strain was crossed with a yellow and round seeds pea strain. All F₁ seeds were yellow and round. In F₂ progenies, statistically large numbers of pea seeds show inheritance according to Mendel’s laws. However, small numbers of seeds could demonstrate other distributions in analysis.

Imagine you get a pea pod from an F₁ plant containing F₂ progeny with 4 pea seeds inside and make guesses about their phenotypes.

You can estimate the probability of a particular phenotype pattern using the following steps:

  1. Find the probability of the particular seeds phenotype combination, based on Mendelian probabilities (1/4, 9/16, etc.)
  2. Find the total number of possible combinations giving that phenotype pattern
  3. Multiply result 1 and result 2.

For example, to calculate the chance of all 4 seeds being yellow: the probability of any one seed being yellow is 3/4, we have 4 independent yellow seeds, and we have only one combination. So P = (3/4)⁴ × 1 = 81/256.

True or false?

Q46.1. The probability of all 4 seeds being green is 1/256.
Q46.2. The probability of 3 round and 1 wrinkled seed is 1.
Q46.3. The probability of 2 green and 2 yellow seeds is 27/128.
Q46.4. The probability of 4 different seed phenotypes in the pod is 243/8192.
Q46.5. The probability of all 4 seeds having identical phenotypes for both traits is 1/32.
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Question reproduced from IBO 2023, Theoretical Paper 2, licensed under CC BY-NC-SA 4.0 - attributed to the International Biology Olympiad. Open the full exam PDF