A driving exam consists of 26 ​multiple-choice questions. Each of the 26 answers is either right or wrong. Suppose the probability that a student makes fewer than 7 mistakes on the exam is 0.29 and that the probability that a student makes from 7 to 18 ​(inclusive) mistakes is 0.58. Find the probability of each of the following outcomes. a. A student makes more than 18 mistakes b. A student makes 7 or more mistakes c. A student makes at most 18 mistakes d. Which two of these three events are​ complementary?

Answer and explanation:Given : A driving exam consists of 26 ​multiple-choice questions. Each of the 26 answers is either right or wrong. Suppose the probability that a student makes fewer than 7 mistakes on the exam is 0.29 and that the probability that a student makes from 7 to 18 ​(inclusive) mistakes is 0.58.Let X be the number of mistake[tex]P(X<7)=P(X\leq 6)=0.29[/tex][tex]P(7\leq X\leq 18)=0.58[/tex]To find : The probability of each of the following outcomes. a) A student makes more than 18 mistakesi.e. [tex]P(X>18)[/tex] [tex]P(X>18)=1-P(X\leq 18)[/tex] [tex]P(X>18)=1-(P(X\leq 6)+P(7\leq X\leq 18))[/tex] [tex]P(X>18)=1-(0.29+0.58)[/tex] [tex]P(X>18)=1-(0.87)[/tex] [tex]P(X>18)=0.13[/tex]b. A student makes 7 or more mistakesi.e. [tex]P(X\geq 7)=1-P(X<7)[/tex][tex]P(X\geq 7)=1-0.29[/tex][tex]P(X\geq 7)=0.71[/tex]c. A student makes at most 18 mistakesi.e. [tex]P(X\leq 18)=1-P(X>18)[/tex]Using 'a' part  [tex]P(X>18)=0.13[/tex][tex]P(X\leq 18)=1-0.13[/tex][tex]P(X\leq 18)=0.87[/tex]d. Which two of these three events are​ complementary?The complement of an event happening is the exact opposite: the probability of it not happening.According to definition,Option a and c are complementary events.