Question

you already know how to use a punnett square to solve a problem such as:
\in pea plants, tall (t) is dominant over short (t). if a plant that is heterozygous for height is crossed with one that is short, what is the probability that an offspring will be short?\
suppose, instead, you are given a problem looking at two traits, instead of one:
\in pea plants, tall (t) is dominant over short (t), and purple flowers (c) is dominant over white (c). if one parent is homozygous dominant for height and heterozygous for flower color, and the other parent is heterozygous for height and has white flowers, what is the probability that an offspring will be tall with white flowers?\

Explanation:

Step1: Determine genotypes

Let \(T\) represent the dominant allele for tall height and \(t\) for short height; \(P\) for purple flower color and \(p\) for white flower color. The cross is between a heterozygous tall - heterozygous purple plant (\(TtPp\)) and a heterozygous tall - white flower plant (\(Ttpp\)).

Step2: Use the product rule

We consider the two traits (height and flower color) separately. For height, the cross \(Tt\times Tt\) gives the following genotypes and ratios: \(TT:Tt:tt = 1:2:1\), and the probability of a heterozygous tall (\(Tt\)) offspring is \(\frac{2}{4}=\frac{1}{2}\). For flower color, the cross \(Pp\times pp\) gives \(Pp:pp=1:1\), and the probability of a white - flowered (\(pp\)) offspring is \(\frac{1}{2}\).

Step3: Calculate combined probability

Using the product rule of probability (since the two traits assort independently), the probability of a heterozygous tall and white - flowered offspring is \(\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)