# 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 , what is the probability that it does not occur?

• A
• B
• C
• D

Q3:

A box contains 56 balls. The probability of selecting at random a red ball is . 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?

• A
• B
• C
• D
• E

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
• B
• C0
• D
• E

Q6:

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

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 denote those who play the piano, those who play the guitar, and those who play the drums.

Using the given diagram, calculate the probability that a student does not play the piano. • A
• B
• C
• D
• E

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 denote rainy days, and let denote hot ones. Use the Venn diagram below to calculate the probability that a day is not rainy. • A
• B
• C
• D
• E

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.

 Airport Percentage of On-time Arrivals El Centro (CA) Baltimore (MD) Charleston (SC) Islip (NY) Milwaukee (WI) 72% 60% 94% 68% 61%
• A, 0.39,
• B, 0.4,
• C, 0.6,
• D, 0.61,
• E, 0.71,