Dr Reasoner has five birthday cards to post and five stamps – two are first class and three are second class.

Two of the birthdays are only two days away and so the cards should have a first class stamp, but the other three are next week so should be fine with a second class stamp.

Unfortunately, Dr Reasoner forgets to put the stamps on the envelopes and has to rely on her housemate to put the stamps on the envelopes and post them.

Her housemate just guesses which stamp to put on which envelope before posting them.

What is the probability that exactly two of the envelopes get the correct stamp? Explain your reasoning carefully!