=+scheme introduced in Section 5.6, we can write the data in this sample as x1 5 1, x2 5 0, x3 5 1, x4 5 0, . . . , x10 5 1, where a “0” indicates that the component functioned correctly and a “1” indicates that it did not work correctly.

Since this data comes from a random sample, we can assume that the outcome involving the first item sampled is independent of the outcome involving the second component sampled, and so forth. Therefore, if  denotes the unknown proportion of defective components in the manufacturing process from which the sample was obtained, then the probability of getting the particular sample can be written as P(x1 5 1 and x2 5 0 and x3 5 1 and…and x10 5 1)

5 P(x1 5 1) P(x2 5 0) P(x3 5 1)…P(x10 5 1)

5 (1 2 )… 5 3

(1 2 )

7 The expression 3

(1 2 )

7