Subjects probability

Probability Interval E5A951

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1. **State the problem:** We need to find the probability that a real number picked randomly from the interval between 2 and 7 lies within that interval. 2. **Understanding the problem:** When picking a real number uniformly from an interval, the probability of picking a number in a sub-interval is the length of that sub-interval divided by the length of the entire interval. 3. **Formula:** Probability $P$ of picking a number in interval $[a,b]$ from $[c,d]$ is given by: $$ P = \frac{b - a}{d - c} $$ 4. **Apply the formula:** Here, the entire interval is $[2,7]$, and the sub-interval is also $[2,7]$ (the same interval). 5. Calculate the lengths: $$ \text{Length of sub-interval} = 7 - 2 = 5 $$ $$ \text{Length of entire interval} = 7 - 2 = 5 $$ 6. Substitute into the formula: $$ P = \frac{5}{5} = 1 $$ 7. **Interpretation:** The probability of picking a real number between 2 and 7 from the interval 2 to 7 is 1, meaning it is certain. **Final answer:** $$ \boxed{1} $$