Question

A driving exam consists of 30 ​multiple-choice questions. Each of the 30 answers is either right or wrong. Suppose the probability that a student makes fewer than 6 mistakes on the exam is 0.28 and that the probability that a student makes from 6 to 20 ​(inclusive) mistakes is 0.53. Find the probability of each of the following outcomes. a. A student makes more than 20 mistakes b. A student makes 6 or more mistakes c. A student makes at most 20 mistakes d. Which two of these three events are​ complementary?

Answer 1

a. P(x>20)=0.19

b. P(x≥6)=0.72

c. P(x≤20)=0.81

d. A and C

Explanation:

We know that:

1) the probability that a student makes fewer than 6 mistakes is 0.28

`P(x<6)=0.28`

2) The probaiblity that a student makes between 6 to 20 mistakes is 0.53.

`P(6\leq x\leq20)=0.53`

We will express the proabilibities in function of the information we have.

a. Probability that a student makes more than 20 mistakes.

`P(x>20)=1-P(x\leq20)=1-(P(x<6)+P(6\leq x \leq20))\\\\P(x>20)=1-(0.28+0.53)=1-0.81=0.19`

b. Probability that the student make 6 or more mistakes

`P(x\geq6)=1-P(Px<6)=1-0.28=0.72`

c. Probability that a student makes 20 mistakes at most

`P(x\leq20)=P(x<6)+P(x\leq x\leq20)=0.28+0.53=0.81`

d. A and C, because A takes a event of more than 20 mistakes and C takes the event of 20 or less mistakes. Both events cover a probability of 1.