Problem No.6 All the fifth-graders in a certain elementary school took a standar

Question

Problem No.6 All the fifth-graders in a certain elementary school took a standardized test. A total of 85% of the students were found to be proficient in reading, 78%were found to be proficient in mathematics, and 65% were found to beproficient in both reading and mathematics. A student is chosen at random. a. What is the probability that the student is proficient in mathematics but not in reading? b. What is the probability that the student is proficient in reading but not in mathematics? c. What is the probability that the student is proficient in neither reading nor Solution

Explanation / Answer

P(proficient in reading) = 0.85

P(proficient in mathematics) = 0.78

P(proficient in both) = 0.65

A) P(proficient in mathematics but not in reading) = P(proficient in mathematics) - P(proficient in both)

= 0.78 - 0.65

= 0.13

B) P(proficient in reading but not in mathematics) = P(proficient in reading) - P(proficient in both)

= 0.85 - 0.65

= 0.2

C) P(proficient in reading or mathematics or both) = P(proficient in reading) + P(proficient in mathematics) - P(probability in both)

= 0.85 + 0.78 - 0.65

= 0.98

P(proficient is neither reading nor mathematics) = 1 - (P(proficient in reading or mathematics or both))

= 1 - 0.98

= 0.02

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.