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$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is

  1. $1/4$
  2. $1/16$
  3. $7/16$
  4. $9/16$
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