GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 11

What is the probability of passing a 10-question true-false exam by random guessing, if a passing score is 70% ?
(A) 0.296094
(B) 0.321502
(C) 0.964506
(D) 0.171875


Answer: (D)

Explanation: You need to get 7,8,9, or 10 problems correct. These are mutually exclusive so we take the sum of the probabilities: p

= p10(7) + p10(8) + p10(9) + p10(10)
= 10C7×(1/2)^7×(1/2)^3 + 10C8×(1/2)^8×(1/2)^2 + 10C9×(1/2)^9×(1/2)^1 + 10C10×(1/2)^10×(1/2)^0 
≈ 0.171875 

Option (D) is correct.

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