In a city, the percentage of left-handed women is 16% and the percentage of left-handed men is 22%. A random sample of five men and five women are selected from the population of the city. What is the probability that the sample contains at least one left-handed woman and one left-handed man.

So yeah, using my awesome calculator I found probabilities of 0 men - 0.2289. 0 women - 0.418. It follows therefore that at least one man - 0.711, one woman - 0.582. My intuition told me that I now have to multiply last two values and even got me the right answer. Could anyone please explain why we multiply 0.711 and 0.582?