GATE CS 2015 Set 1 — Question 5
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Engineering Mathematics → Probability & Statistics → Sample Space & Events
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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?
Correct answer
(A) 0.20
Solution
To find the probability that the sum of the two randomly selected numbers (one from Set and one from Set ) equals , we determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Find the Total Number of Possible Outcomes
Let and .- The number of elements in Set is .
- The number of elements in Set is .
Step 2: Find the Number of Favorable Outcomes
We need to find the pairs such that , where and .Let us check the possible values for :- If , then (which is in ). is a valid pair.
- If , then (which is in ). is a valid pair.
- If , then (which is in ). is a valid pair.
- If , then (which is in ). is a valid pair.
Step 3: Calculate the Probability
The probability that the sum of the two numbers equals is given by:Correct Option: AContinue learning with Success Tracker
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