# Using the Addition Rule for Disjoint Events

• 1.

Find the probability of drawing a spade or a red card from a standard deck of cards.

Answers:

• {eq}\dfrac{3}{2} {/eq}

• {eq}\dfrac{3}{4} {/eq}

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{1}{4} {/eq}

• 2.

In a lottery of 14 tickets numbered from 1 to 14, one ticket is drawn. Find the probability that the drawn ticket is either a multiple of 3 or 5.

Answers:

• {eq}\dfrac{5}{14} {/eq}

• {eq}\dfrac{8}{14} {/eq}

• {eq}\dfrac{5}{7} {/eq}

• {eq}\dfrac{3}{7} {/eq}

• 3.

A bag contains 5 red balls, 3 blue balls, 7 green balls, and 4 purple balls. What is the probability that a ball drawn from the bag is blue or green?

Answers:

• {eq}\dfrac{7}{19} {/eq}

• {eq}\dfrac{4}{19} {/eq}

• {eq}\dfrac{3}{19} {/eq}

• {eq}\dfrac{10}{19} {/eq}

• 4.

A box contains 100 red cards, 50 blue cards, and 150 yellow cards. Find the probability that if a card is drawn it is either a red card or a blue card.

Answers:

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{1}{6} {/eq}

• {eq}\dfrac{1}{50} {/eq}

• {eq}\dfrac{1}{3} {/eq}

• 5.

A die is thrown once. Find the probability that the number obtained on a die is either an odd number or an even number.

Answers:

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{2}{3} {/eq}

• {eq}1 {/eq}

• {eq}0 {/eq}

• 6.

Cards marked with numbers 3 to 20 are placed in a box. One card is drawn from the box. Find the probability that the number on the card is either a prime number or an even number.

Answers:

• {eq}\dfrac{11}{18} {/eq}

• {eq}\dfrac{4}{5} {/eq}

• {eq}\dfrac{8}{9} {/eq}

• {eq}\dfrac{1}{9} {/eq}

• 7.

From a class of 25 students with roll numbers 1 to 25, a student is selected at random for a quiz competition. What is the probability that the roll number of the selected student is either a multiple of 5 or 7?

Answers:

• {eq}\dfrac{18}{25} {/eq}

• {eq}\dfrac{11}{25} {/eq}

• {eq}\dfrac{8}{25} {/eq}

• {eq}\dfrac{2}{25} {/eq}

• 8.

A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is either a 10 or a queen.

Answers:

• {eq}\dfrac{11}{52} {/eq}

• {eq}\dfrac{5}{52} {/eq}

• {eq}\dfrac{4}{52} {/eq}

• {eq}\dfrac{2}{13} {/eq}

• 9.

What is the probability of drawing a red or green marble from a bowl of five differently-colored (red, green, yellow, blue, and purple) marbles?

Answers:

• {eq}\dfrac{1}{5} {/eq}

• {eq}\dfrac{2}{5} {/eq}

• {eq}\dfrac{3}{5} {/eq}

• {eq}\dfrac{4}{5} {/eq}

• 10.

A pair of dice is rolled and the numbers that come up are recorded. Find the probability that either the sum is greater than 8 or a 2 occurs on at least one of the dice.

Answers:

• {eq}\dfrac{7}{12} {/eq}

• {eq}\dfrac{17}{36} {/eq}

• {eq}\dfrac{23}{52} {/eq}

• {eq}\dfrac{5}{13} {/eq}

• 11.

Three coins are tossed once. Find the probability of getting three heads or three tails.

Answers:

• {eq}1 {/eq}

• {eq}\dfrac{3}{8} {/eq}

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{1}{4} {/eq}

• 12.

In a single throw of a die, find the probability of getting the number 4 or a multiple of 3.

Answers:

• {eq}\dfrac{2}{3} {/eq}

• {eq}\dfrac{1}{3} {/eq}

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{5}{6} {/eq}

• 13.

From a deck of 52 cards, a card is drawn. What is the probability of drawing a black king or a card of hearts?

Answers:

• {eq}\dfrac{8}{52} {/eq}

• {eq}\dfrac{15}{52} {/eq}

• {eq}\dfrac{6}{52} {/eq}

• {eq}\dfrac{13}{52} {/eq}

• 14.

In a single throw of a pair of dice, find the probability of getting a doublet or a sum of 7.

Answers:

• {eq}\dfrac{1}{12} {/eq}

• {eq}\dfrac{1}{3} {/eq}

• {eq}\dfrac{15}{36} {/eq}

• {eq}\dfrac{7}{36} {/eq}

• 15.

The milk party is prepared for students. 15 students drink only banana milk, 8 students drink only almond milk, 6 students drink only whole milk, and 3 students drink only soy milk. What is the probability that a student drinks only almond or soy milk?

Answers:

• {eq}\dfrac{14}{32} {/eq}

• {eq}\dfrac{8}{32} {/eq}

• {eq}\dfrac{11}{32} {/eq}

• {eq}\dfrac{10}{32} {/eq}

• 16.

At a coaching center, there are 40 students. 15 students are excellent in mathematics, 16 students are average in mathematics and 9 students are poor in mathematics. What is the probability that a student randomly selected for a quiz is excellent or average in mathemtics?

Answers:

• {eq}\dfrac{1}{40} {/eq}

• {eq}\dfrac{31}{40} {/eq}

• {eq}\dfrac{16}{40} {/eq}

• {eq}\dfrac{15}{40} {/eq}

• 17.

In a survey of 60 people, 38 consider themselves republicans, 17 consider themselves democrats, and the rest are considered independent. Find the probability that the person selected at random will be a republican or independent.

Answers:

• {eq}\dfrac{17}{60} {/eq}

• {eq}\dfrac{38}{60} {/eq}

• {eq}\dfrac{43}{60} {/eq}

• {eq}\dfrac{5}{60} {/eq}

• 18.

A survey was conducted at a university. It was found that 15 students like to read thriller novels only, 13 students like to read mystery novels only, and 5 students like to read romantic novels only. What is the probability that a student selected at random likes to read thrillers or romance novels?

Answers:

• {eq}\dfrac{5}{33} {/eq}

• {eq}\dfrac{15}{33} {/eq}

• {eq}\dfrac{20}{33} {/eq}

• {eq}\dfrac{10}{33} {/eq}

• 19.

A group of 20 girls was surveyed. 5 are interested in taking part in classical dance, 6 are interested in taking part in games, 7 are interested in taking part in bhangra and the rest are not interested in taking part in any activity. What is the probability that a girl chosen randomly is interested in classical dance or bhangra?

Answers:

• {eq}\dfrac{1}{10} {/eq}

• {eq}\dfrac{3}{5} {/eq}

• {eq}\dfrac{1}{4} {/eq}

• {eq}\dfrac{6}{20} {/eq}

• 20.

250 farmers of a village were surveyed. It was observed that 160 farmers grow wheat only, 65 farmers grow sugarcane only, and 25 farmers grow rice only. What is the probability that a farmer selected at random from the village grows wheat or rice?

Answers:

• {eq}\dfrac{160}{250} {/eq}

• {eq}\dfrac{37}{50} {/eq}

• {eq}\dfrac{37}{250} {/eq}

• {eq}\dfrac{185}{50} {/eq}

• 21.

Find the probability of getting a face card or a number 9 from a well-shuffled pack of 52 cards.

Answers:

• {eq}\dfrac{3}{52} {/eq}

• {eq}\dfrac{5}{13} {/eq}

• {eq}\dfrac{4}{13} {/eq}

• {eq}\dfrac{1}{4} {/eq}

• 22.

In a class of 23 students, 13 students like to play cricket only, 6 like to play badminton only and 4 students like to play football only. Find the probability that a student selected at random likes to play cricket or badminton.

Answers:

• {eq}\dfrac{13}{23} {/eq}

• {eq}\dfrac{19}{23} {/eq}

• {eq}\dfrac{18}{23} {/eq}

• {eq}\dfrac{4}{23} {/eq}

• 23.

What is the probability of getting a sum less than 4 or getting a sum greater than 11 when throwing a pair of dice?

Answers:

• {eq}\dfrac{1}{9} {/eq}

• {eq}\dfrac{4}{13} {/eq}

• {eq}\dfrac{2}{9} {/eq}

• {eq}\dfrac{5}{36} {/eq}

• 24.

Balls marked with numbers 51 to 100 are placed in a jar. A ball is drawn at random. What is the probability that the number that is marked on the ball is divisible by either 10 or 11?

Answers:

• {eq}\dfrac{1}{5} {/eq}

• {eq}\dfrac{2}{25} {/eq}

• {eq}\dfrac{2}{5} {/eq}

• {eq}\dfrac{1}{25} {/eq}

• 25.

A student is selected at random from a class of 35 students where 10 students liked to eat pizza only, 14 students liked to eat burgers only, 6 students like to eat popcorn only and 5 students like to eat Maggi only. What is the probability that a selected student likes to eat pizza or Maggi?

Answers:

• {eq}\dfrac{2}{7} {/eq}

• {eq}\dfrac{4}{7} {/eq}

• {eq}\dfrac{3}{7} {/eq}

• {eq}\dfrac{5}{7} {/eq}

• 26.

In a hospital, there are 50 people, out of which 4 are doctors, 35 are patients and the rest are nurses. What is the probability that a person chosen at random will be a doctor or nurse?

Answers:

• {eq}\dfrac{1}{8} {/eq}

• {eq}\dfrac{39}{50} {/eq}

• {eq}\dfrac{1}{10} {/eq}

• {eq}\dfrac{3}{10} {/eq}

• 27.

Two coins are tossed simultaneously. What is the probability of getting two heads or two tails?

Answers:

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{3}{4} {/eq}

• {eq}\dfrac{1}{4} {/eq}

• {eq}1 {/eq}

• 28.

Let us suppose we have a deck of standard playing cards. A card is drawn from this deck. Find the probability that the card drawn is either an ace or a king.

Answers:

• {eq}\dfrac{17}{52} {/eq}

• {eq}\dfrac{2}{52} {/eq}

• {eq}\dfrac{2}{13} {/eq}

• {eq}\dfrac{14}{52} {/eq}

• 29.

Out of 40 teachers, 13 can teach chemistry only, 15 can teach statistics only, and 12 can teach physics. A teacher is selected at random for taking a class. What is the probability that a selected teacher teaches chemistry or physics?

Answers:

• {eq}\dfrac{5}{8} {/eq}

• {eq}\dfrac{1}{40} {/eq}

• {eq}\dfrac{3}{10} {/eq}

• {eq}\dfrac{5}{20} {/eq}

• 30.

What is the probability that a number picked from 1 to 20 is an odd or an even number?

Answers:

• {eq}\dfrac{1}{2} {/eq}

• {eq}\dfrac{13}{20} {/eq}

• {eq}0 {/eq}

• {eq}1 {/eq}

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