Adults and high school students were asked trivia questions

Adults and high school students were asked trivia questions. The number of correct answers given by each participant was recorded. The data table is provided below.

a) What is the probabilty that a randomly selected participant is a student?

b) What is the probabilty that a randomly selected participant has fewer than 2 correct answers?

c) What is the probabilty that a randomly selected participant is an adult or had no correct answers?

d) What is the probabilty that a randomly selected participant is an adult and had all four correct answers?

Number of Correct Answers 3 2 Total Adults Students Total 147 14 295 7 26 35 4534 43 12 7 45 41 7 4541 50 38 42 90 75

Solution

a)

Probability that is a student = number total of students / total of the partipipant

Probability that is a student = 148 / 295

Probability that is a student = 0.5017

b)

Probability that has fewer than 2 correct answer = P(0) + P(1)

P(correct 0 answer ) = 50 / 295 = 0.1695

P( correct 1 answer ) = 38 / 295 = 0.1288

P ( fewer than 2 correct answer ) = 0.1695+0.1288 = 0.2383

c)

P( adult or had no correct answer ) = P(adult ) + P( had no correct answer) - P( adult and no correct answer)

P( adult) = 147 / 295 = 0.4983

P( had no correct answer) = 50 / 295 = 0.1695

P( adult and no correct answer) = 7 / 295 = 0.0237

P( adult or had no correct answer ) = 0.4983 + 0.1695 - 0.0237

P( adult or had no correct answer ) = 0.6441

d)

P ( adult and had 4 correct answer ) = 34 / 295

P ( adult and had 4 correct answer ) = 0.1152