$A$ 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
Meeting occurs if the first person arrives between $1:00$ and $1:45$ and the second person arrives in the next $15$ minutes or if both the persons arrive between $1:45$ and $2:00.$
So, probability of a meet $= 3/8 + 1/16 = 7/16$
Correct Answer: $C$
But in 1:45 to 2:00
If A comes first then B Or B comes first then A
doen't this count to two diff cases ??
For such questions which are also known as probability based on areas , u can find easily using grid of 2 dimension as shown below
The favorable area for the given problem is shown above...
So no of favourable cells = 4 + 6 * 1/2 = 7
Therefore probability that they meet = No of favourable cells/ No of total cells
= 7 / 16
Hence C) should be the correct option.