A man 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. Resourcesful, 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. What is the probability that the door opens with the third key

The value is  

Step-by-step explanation:

From the question we are told that

   The number of keys is  n

    The number of keys remaining after the first key is chosen is  n-1

    The probability that he gains entrance with the first key he selects is

      Generally the probability that the first key does not open the door is

      Generally the number of keys remaining after the second key is chosen is  

         n-2

      Generally the probability that he gains entrance with the second key he selects is

       Generally the probability that the second key does not opens the door is

   Generally the probability that he gains entrance with the third key he selects is

Generally the probability that the door opens with the third key

=>      

=>        

Note :  

      All the outcome of the events are independent

b

step-by-step explanation:

the total is 23.97. 0.25% is off so you have to subtracting 25% from 100% and you will get 75% if you convert it to decimal you will get 0.75. you have to find the original because the formula is % times original = total.so you have the total and the % so you just have to plug it in.

step-by-step explanation: