Use the uniform distribution. Suppose that a random variable X follows the uniform distribution described in Example 4.26 (pages 213–214). For each of the following events, find the probability and illustrate your calculations with a sketch of the density curve similar to the ones in Figure 4.12 (page 214).

(a) The probability that X is less than 0.1.

(b) The probability that X is greater than or equal to 0.8.

(c) The probability that X is less than 0.7 and greater than 0.5.

(d) The probability that X is 0.5.