hunterdylan01
30.09.2019 •
Mathematics
Aman has n keys on a key ring, one of which opens the door to his apartment. having celebrated a bit too much one evening, he returns home only to find himself unable to distinguish one key from another. resourceful, he works out a fiendishly clever plan: he will choose a key at random and try it. if it fails to open the door, he will discard it and choose at random one of the remaining n−1 keys, and so on. clearly, the probability that he gains entrance with the first key he selects is 1/n. show that theprobability the door opens with the third key he tries is also 1/n.
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Ответ:
Answer and Step-by-step explanation:
The probability that he gains entrance with the first key he selects is 1/n. Show that theprobability the door opens with the third key he tries is also 1/n.
get in 1st try
right key = 1
keys in the chain: n
p = 1/n
get in 3rd try means wrong key 1st try and wrong key 2nd try:
wrong keys 1st try = n - 1
keys not tried in the chain = n
wrong keys 2nd try = n - 2
keys not tried in the chain = n - 1
right key 3rd try = 1
keys not tried in the chain = n - 2
1st 2nd 3rd
n-1/n * n-2/n-1 * 1/n-2 = 1/n
Ответ:
a
step-by-step explanation: