Correct : 0.74

Explanation:
1. Let X be the random point chosen uniformly over (0,1). The probability density function of X is f(x) = 1 for 0 < x < 1.
2. The point X splits the interval into two pieces: (0, X) and (X, 1). The subinterval containing 0.4 depends entirely on where X falls:
• If X ≤ 0.4, then 0.4 lies in the right subinterval (X, 1), which has a length of: 1 - X
• If X > 0.4, then 0.4 lies in the left subinterval (0, X), which has a length of: X
3. The expected length E[L] is calculated by integrating these lengths over their respective intervals:
    E[L] = ∫₀^0.4 (1 - x) dx + ∫_0.4¹ x dx
4. Evaluating the first part (from 0 to 0.4):
    [x - x²/2]₀^0.4 = (0.4 - 0.4²/2) - 0 = 0.4 - 0.08 = 0.32
5. Evaluating the second part (from 0.4 to 1):
    [x²/2]_0.4¹ = (1²/2) - (0.4²/2) = 0.5 - 0.08 = 0.42
6. Adding both parts together gives the total expected length:
    E[L] = 0.32 + 0.42 = 0.74