1 votes 1 votes There are 20 locks and 20 matching keys. Maximum number of trials required to match all the locks is (a) 190 (b) 210 (c) 400 (d) 40 Probability engineering-mathematics isro-mech probability + – sh!va asked Mar 7, 2017 • retagged Mar 8, 2019 by Naveen Kumar 3 sh!va 838 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes 1st key, try all $20$ locks. Assume $19$ trials fail. $20$th lock will automatically match. 2nd key, try remaining $19$ locks. Assume all $18$ trials fail. $19$th lock will match. So on ... Total maximum trials = $\begin{align*} \sum_{k=1}^{19} k = 190 \end{align*}$ dd answered Mar 7, 2017 • selected Mar 7, 2017 by srestha dd comment Share Follow See 1 comment See all 1 1 comment reply Akriti sood commented Mar 7, 2017 reply Follow Share why u considered 19 trials for first key?should'ne it be 20?? will u nt consider that trial in which key got matched to the lock?? 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Question asks for maximum number of trials For first lock, maximum trials occur when all 19 keys do not match and last key matches. So 20 trials Similarly 19 trials for next lock Total number of trials = 20+19+.....+1= 20*21/2 =210 sh!va answered Mar 7, 2017 sh!va comment Share Follow See all 0 reply Please log in or register to add a comment.
