A sportsperson could be an expert in badminton and / or squash. Given that someone is a squash expert, the probability that they are expert at badminton as well is 0.8. There are twice as many badminton experts as there are squash experts. Given that Saina is a badminton expert, what is the likelihood that she is an expert in squash?

Let P(B) be the probability of a sportsperson being an expert in badminton, and P(S) be the probability of a sportsperson being an expert in squash.

Using Bayes' Theorem, we get 

$$\ P(B|S)\ =\frac{P\left(B\ ∩\ S\right)}{P\left(S\right)}=0.8$$

$$P\left(B\ ∩\ S\right)=0.8\ P\left(S\right)$$

It is given that there are twice as many badminton experts as there are squash experts.

$$P\left(B\right)=2P\left(S\right)$$

So, $$P\left(B\ ∩\ S\right)=0.4\ P\left(B\right)$$

Given that Saina is a badminton expert, the likelihood that she is an expert in squash will be given by P(S|B).

$$\frac{P\left(B\ ∩\ S\right)}{P\left(B\right)}$$ = 0.4

$$\ P(S|B)\ = 0.4$$

Option A is correct.