If two numbers p and q are chosen randomly from the set 1,2,3,4 , one by one, with replacement, then the probability of getting p^2>4 q is

Step-by-step solution

Two numbers are selected with replacement from S = 1,2,3,4 , giving 4 4 = 16 total ordered pairs (p,q) . The condition p^2 4q is analyzed: When p=1 , p^2=1 ; no q satisfies 1 4q . When p=2 , p^2=4 ; the condition 4 4q holds only for q=1 . When p=3 , p^2=9 ; 9 4q yields favorable q 1,2 . When p=4 , p^2=16 ; all q 1,2,3,4 satisfy 16 4q . The number of favorable outcomes is 0 + 1 + 2 + 4 = 7 . The probability is 7 16 , corresponding to option B .