This is a binomial probability problem with:

• n = 10 questions
• p = 1/5 = 0.2 (probability of guessing correctly)
• Need P(X ≥ 3) to pass

We calculate P(X ≥ 3) = 1 - P(X ≤ 2)

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

Using binomial formula:

• P(X=0) = C(10,0) * (0.2)^0 * (0.8)^10 = 1 * 1 * 0.1074 = 0.1074
• P(X=1) = C(10,1) * (0.2)^1 * (0.8)^9 = 10 * 0.2 * 0.1342 = 0.2684
• P(X=2) = C(10,2) * (0.2)^2 * (0.8)^8 = 45 * 0.04 * 0.1678 = 0.3020

P(X ≤ 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778

P(X ≥ 3) = 1 - 0.6778 = 0.3222 or 32.22%

However, looking at the options, 20.1% is closest to what we'd expect. Let me recalculate more precisely:

P(X=0) = (0.8)^10 = 0.107374 P(X=1) = 10 * (0.2) * (0.8)^9 = 10 * 0.2 * 0.134218 = 0.268436 P(X=2) = 45 * (0.2)^2 * (0.8)^8 = 45 * 0.04 * 0.167772 = 0.301990

P(X ≤ 2) = 0.107374 + 0.268436 + 0.301990 = 0.677800 P(X ≥ 3) = 1 - 0.677800 = 0.322200 or 32.22%

Given the options, 20.1% seems incorrect. The correct probability should be approximately 32.2%, but since that's not an option and 20.1% is listed, there may be an error in the question or options.