GATE CSE 2015 Set 1 | Question: GA-3‏

Question

Given Set $A= {2, 3, 4, 5}$ and Set $B= { 11, 12, 13, 14, 15}$, two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals $16$?

• A. $0.20$
• B. $0.25$
• C. $0.30$
• D. $0.33$

Answer 1

option A because total combinations are $5\times 4=20$ and out of $20$ we have only $4$ combinations which have sum $16$

1. $2,14$
2. $3.13$
3. $4.12$
4. $5,11$

Comments

@Lakshman Patel RJIT

(2,14)  (14,2)
(3.13)  (13,3)
(4.12)  (12,4)
(5,11)  (11,5)

This will also be correct

8 / 40 ==>0.2

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yes ,set does not contain duplicate

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Case: Two dices are thrown, what is the probability that sum is 5. Then why we consider (2,3) and (3,2) as different cases !

I think @Lakshman Patel RJIT, query is legitimate and @jatin khachane 1’s solution seems suitable.

Answer 2

option A

probability =Number of favorable case/total case

The favorable cases are:-

2,14
3.13
4.12
5,11 

4C1=4

total case =A number selected from set A * A number selected from set B

  4C1*5C1=20 

probability =Number of favorable case/total case=4/20=0.20

Answer 3

After choosing an element from A, there is only one element in B out of 5 elements that makes sum 16.

So, 1/5 = 0.2

Answer 4

Solution: A
The total number of pairs possible is 20(with 1 element from A and 1 element from B). The pairs which sum to 16 are 4nos, that are (2,14)(3,13)(4,12)(5,11). So 4/20 =0.20