GATE2012 CY: GA-7

Question

$A$ 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

• A. $1/4$
• B. $1/16$
• C. $7/16$
• D. $9/16$

Answer 1

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 $2:00.$ 

Case 1:

• $45/60$ are favourable cases and hence probability of first person arriving between $1:00$ and $1:45$ is $3/4.$ 
• Probability of second person arriving in the next $15$ minutes $= 15/60 = 1/4$
• So, probability of one person arriving between $1:00$ and $1:45$ and meeting the other $= 3/4 \times 1/4 \times 2 = 3/8$ $(2$ for choosing the first arriving friend$)$ 

Case 2:

• Both friends must arrive between $1:45$ and $2:00.$ Probability $= 1/4 \times 1/4 = 1/16.$

So, probability of a meet $= 3/8 + 1/16 = 7/16$

Correct Answer: $C$

Comments

why not in second case u did 2C1?

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For the second case both have to arrive after 1:45- we do not have a choice here. In the first case, we have an order- first arriving can be one among 2.

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@Arjun sir,

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 ??

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What if both arrive together in the 1^st case ?

Answer 2

Check this

Comments

@Kajal , nice answer...

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Best one :)

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This is much more intuitive !!

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nice answer! can connect all the conditions in a single graph.

Answer 3

probability that one person meet on that day = 15/60 = 1/4
Prob(failing to meet) = 3/4
prob(failing to meet by both the persons) = 3/4 * 3/4 = 9/16
Prob( meet on that day by both the persons) = 1-9/16 = 7/16

Answer 4

For such questions which are also known as probability based on areas , u can find easily using grid of 2 dimension as shown below

		1/2*F	F
	1/2 * F	F	1/2 * F
1/2*F	F	1/2 * F
F	1/2 * F

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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.

Comments

THIS IS WRONG ANSWER  CORRECT ANSWER IS 7/16

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Corrected..:)

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Hi habib could you explain it bit more.

We are unable to understand what those cells in table are representing ..?