Consider the bar code 39 is a common bar code system that consists of narrow and wide bars (black) separated by either wide or narrow spaces (white). Each character contains nine elements (five bars and four spaces). The code for a character starts and ends with a bar (either narrow or wide) and a (white) space appears between each bar. The original specification (since revised) used exactly two wide bars and one wide space in each character. For example, if b and B denote narrow and wide (black) bars, respectively, and w and W denote narrow and wide (white) spaces, a valid character is bwBwBWbwb (the number 6).. Suppose that all 40 codes are equally likely (none is held back as a delimiter).

Determine the probability for each of the following:

(a) The second bar is wide given that the first bar is wide.

(b) The third bar is wide given that the first two bars are not wide.

(c) The first bar is wide given that the last bar is wide.