Answer :
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 mistakes
i.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 mistakes
i.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 mistakes
i.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.