Question

A plant is heterozygous and is designated as Aa. It produces two types of gametes A and a. The possibility of ‘a’ gamete fertilising A or a is:
A) $\dfrac{1}{2}$
B) $\dfrac{1}{4}$
C) $\dfrac{1}{6}$
D) $\dfrac{1}{1}$
E) $\dfrac{1}{1}$

Answer 1

Hint: The chance of one gamete fertilizing another depends on whether the two events are mutually exclusive or follow each other. Depending on that the addition or multiplication rules of statistics would apply.

Complete answer:
The plant will thus produce male gametes (microspores) A and a, and female gametes (megaspores) A and a. If microspore A is fertilising the megaspore gametes A and a, it will produce AA or Aa, which are two possibilities, therefore the probability of either event is $\dfrac{1}{2}$.

Similarly, microspore would fertilise megaspore A or a to give either aA or aa, and the probability of each event is again $\dfrac{1}{2}$. The two events are mutually exclusive; therefore the multiplication rule applies which gives us $\dfrac{1}{2}\times\dfrac{1}{2}$ or $\dfrac{1}{4}$. Option B is the correct answer.

>If we are considering only the probability of only the microspore a gametes fertilising A or a, then the answer would be option (A) or $\dfrac{1}{2}$. Option A is incorrect.
>Option C is not correct, as the individual probabilities are not divisible by 3.
>For option D to be incorrect, it would mean that there is a 100 percent chance of all events happening, which is not possible, It can only be one or the other. One gamete cannot simultaneously fertilise two. Option D is incorrect.
>Option E is incorrect as one gamete would fertilise one or the other at some point. It does not have a zero chance.

Hence the correct answer is option ‘B’.

Note: In a heterozygous plant, during sexual reproduction, both the androecium and the gynoecium will produce gametes which are either A or a. which is why we consider the possibility of both microspore a fertilising both female gametes, and vice versa.