Convolution of independent but 'different' probability distributions

Question

I have the following two probability distributions they relate to a particular ice-cream:

GenderProbabilities = {
    male:   0.5,
    female: 0.5,
}

AgeProbabilities = {
    young: 0.4,
    old:   0.6
}

So the tables describe the probability that the next customer will be male or female and if they are either young or old. A colleague claims that we can apply convolution to these tables and get something "meaningful" to describe this particular ice-cream. So I run the following in R:

convolve(c(0.5, 0.5), rev(c(0.4, 0.6)), type="o")

Which gives

0.2 0.5 0.3

However, I ask my colleague what does this actually mean and they are unable to respond. According to the definition on wikipedia it would mean something like:

{
    male + young                     : 0.2,
    (female + young) | (male + old)  : 0.5,
    female + old                     : 0.3
}

Is this interpretation correct?