Probability of Letters in Envelopes: A1, A2, A3, A4, A5

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The discussion focuses on the probability calculations related to letters being placed in envelopes by Mr. X's son. The probabilities for various scenarios are established: A1 receiving his letter has a probability of 1/5, while both A1 and A2 receiving their letters together has a probability of 1/20. The probability of A1 receiving his letter while A2 does not is calculated as 3/20. Additionally, the probability that at least one of A1, A2, or A3 receives their letter is determined to be 3/5, while the probability that no one receives their letter is confirmed to be 1/5.

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Scenario: Mr. X is writing letters to five persons A1, A2, A3, A4, A5. After Mr. X has written them he has to leave the room where the letters and envelopes are. Mr X's son, who can't read, decides to help his dad and puts each letter in different envelopes. What is the probability that:

a) A1 gets his letter
P = 1/5.

b) A1 and A2 both gets their letters
P = (1/5)(1/4) = 1/20.

c) A1 gets his letter and A2 doesn't get his
P = (1/5)(3/4) = 3/20.

d) at least one of A1, A2, A3 gets his/their letter
Need help with this one.
P = 1 - (4/5)(3/4)(2/3) = 1 - 2/5 = 3/5 ?

e) no one gets their letter
P = 4!/5! = 1/5.
 
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