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
GATE 2015 · General Aptitude · Probability · medium
Answer: P(a + b = 16) = 4/20 = 0.20. Answer: A.
Compute the total sample space: |A| = 4, |B| = 5 => Total = 4 * 5 = 20 equally likely pairs.
Identify favorable pairs (a + b = 16): a=2 => b=14 (in B); a=3 => b=13 (in B); a=4 => b=12 (in B); a=5 => b=11 (in B). All four values are in B. Favorable count = 4.
Calculate the probability: P = 4 / 20 = 1/5 = 0.20