1. **Problem statement:** We are given a probability distribution over the interval from 0 to 10, divided into regions A, B, C, and D with areas 0.10, 0.30, 0.45, and 0.15 respectively. 2. **Goal:** Find the probability that a real number between 0 and 4 is picked. 3. **Key concept:** The probability of selecting a number in a certain interval corresponds to the area under the probability density curve over that interval. 4. **Given areas:** - Region A covers from 0 to 2 with area 0.10 - Region B covers from 2 to 4 with area 0.30 5. **Calculate probability for 0 to 4:** $$P(0 \leq X \leq 4) = P(A) + P(B) = 0.10 + 0.30 = 0.40$$ 6. **Answer:** The probability that a real number between 0 and 4 is picked is **0.40**.