Lesson Worksheet: Complementary Events Mathematics • 10th Grade

In this worksheet, we will practice finding the probability of complementary events.

Q1:

If the probability that a student passes in mathematics is 0.7, what is the probability that the student fails?

Q2:

If the probability of an event occurring is 1336, what is the probability that it does not occur?

  • A2336
  • B1372
  • C1336
  • D2372

Q3:

A box contains 56 balls. The probability of selecting at random a red ball is 57. How many balls in the box are not red?

Q4:

A box contains 10 red marbles, 3 white marbles, and 17 blue marbles. If a marble is picked from the box at random, what is the probability that the marble is not blue?

  • A110
  • B23
  • C13
  • D1330
  • E910

Q5:

The days in a certain month were classified into rainy days and clear days. Find the probability that a day is clear using the given diagram.

  • A1
  • B1415
  • C0
  • D1315
  • E115

Q6:

The students in a music class either play piano, guitar, or both, while some play neither piano nor guitar. Let 𝐴 denote the students who play piano, and let 𝐵 denote the students who play guitar. Use the given diagram to calculate the probability that a student does not play guitar.

  • A623
  • B1523
  • C823
  • D1723
  • E423

Q7:

In a music class, students learn to play the piano, the guitar, and the drums. Some students play 2 instruments, some play all 3 instruments, and some play none of the instruments. Let 𝑃 denote those who play the piano, 𝐺 those who play the guitar, and 𝐷 those who play the drums.

Using the given diagram, calculate the probability that a student does not play the piano.

  • A831
  • B2231
  • C415
  • D931
  • E2131

Q8:

The days in a certain month are classified as rainy days, hot days, both rainy and hot days, or neither rainy nor hot days. Let 𝑅 denote rainy days, and let 𝐻 denote hot ones. Use the Venn diagram below to calculate the probability that a day is not rainy.

  • A45
  • B15
  • C215
  • D1315
  • E12

Q9:

The table represents the data collected from 200 conference attendees of different nationalities:

Speak ArabicSpeak EnglishSpeak FrenchTotal Sum
Man 45 35 45 125
Woman 40 30 5 75
Sum 85 65 50 200

Find the probability that a randomly selected participant does NOT speak English.

Q10:

The table shows the percentage of flights which arrived on time at several airports. If a flight due to land at Baltimore Airport (MD) is randomly selected, determine the probability that the flight will NOT arrive on time, expressing your answer as a percent, a decimal, and a fraction.

AirportEl Centro (CA)Baltimore (MD)Charleston (SC)Islip (NY)Milwaukee (WI)
Percentage of On-time Arrivals72%60%94%68%61%
  • A39%, 0.39, 39100
  • B40%, 0.4, 25
  • C60%, 0.6, 35
  • D61%, 0.61, 61100
  • E71%, 0.71, 71100

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