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Lesson: Finding the Probability of Mutually Exclusive and Non-Mutually Exclusive Events

Question Video: Determining the Union of Two Mutually Exclusive Events

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Worksheet: Finding the Probability of Mutually Exclusive and Non-Mutually Exclusive Events • 22 Questions

Q1:

Determine the probability of rolling 1, 2, 3, or 6 on a six-sided die.

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Q2:

Determine the probability of rolling 1 or 2 on a six-sided die.

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Q3:

Determine the probability of rolling 3 or 6 on a six-sided die.

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Q4:

Suppose that and are two mutually exclusive events. The probability of the event occurring is five times that of the event occurring. Given that the probability that one of the two events occurs is 0.18, find the probability of event occurring.

Q5:

If a die is rolled once, then what is the probability of getting an odd and an even number together?

Q6:

A bag contains fifty-one balls numbered 1 to 51. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 17 or 27? Give your answer as a fraction in its simplest form.

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Q7:

A bag contains fifty-one balls numbered 1 to 76. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 57 or 66? Give your answer as a fraction in its simplest form.

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Q8:

A bag contains fifty-one balls numbered 1 to 61. If one ball is randomly drawn from the bag without looking, what is the probability that is is numbered 58 or 59? Give your answer as a fraction in its simplest form.

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Q9:

A bag contains red, blue, and green balls, and one is to be selected without looking. The probability that the chosen ball is red is equal to seven times times the probability that the chosen ball is blue. The probability that the chosen ball is blue is the same as the probability that the chosen ball is green.

Find the probability that the chosen ball is red or green.

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Q10:

Suppose that and are two mutually exclusive events. The probability of the event occurring is four times that of the event occurring. Given that the probability that one of the two events occurs is 0.6, find the probability of event occurring.

Q11:

A small choir has a tenor singer, 3 soprano singers, a baritone singer, and a mezzo-soprano singer. If one of their names was randomly chosen, determine the probability that it was the name of the tenor singer or soprano singer.

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Q12:

A small choir has a tenor singer, a soprano singer, a baritone singer, and 3 mezzo-soprano singers. If one of their names was randomly chosen, determine the probability that it was the name of the tenor singer or mezzo-soprano singer.

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Q13:

A bag contains 41 balls. There are 28 red balls which are numbered 1 to 28 and 13 white balls which are numbered 29 to 41. If a ball is chosen from the bag at random, what is the probability of the ball being red and having an even number?

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Q14:

A bag contains 44 balls. There are 10 red balls which are numbered 1 to 10 and 34 white balls which are numbered 11 to 44. If a ball is chosen from the bag at random, what is the probability of the ball being white and having an odd number?

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Q15:

A deck of cards numbered 1 to 35 is shuffled and a card is chosen. What is the probability that the chosen card has a number which is divisible by 8 and 6?

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Q16:

A survey asked 49 people if they had visited any clubs recently. 28 had attended Club A, 38 had attended Club B, and 8 had not been to either club What is the probability that a random person from the sample attended both clubs?

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Q17:

A deck of cards numbered 1 to 67 is shuffled and a card is chosen. What is the probability that the chosen card has a number which is divisible by 2 and 5?

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Q18:

A deck of cards numbered 1 to 55 is shuffled and a card is chosen. What is the probability that the chosen card has a number which is divisible by 4 and 5?

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Q19:

The probability that a student passes their physics exam is 0.71. The probability that they pass their mathematics exam is 0.81. The probability that they pass both exams is 0.68. What is the probability that the student only passes their mathematics exam?

Q20:

The probability that a student passes their physics exam is 0.54. The probability that they pass their mathematics exam is 0.86. The probability that they pass both exams is 0.51. What is the probability that the student only passes their mathematics exam?

Q21:

In an experiment a coin is flipped and a die rolled once, then the upper face of each is observed. is the event that the coin lands head side up and the die lands showing a prime number. is the event that the die lands showing an even number. Find the probability of the occurrence of the two events and together.

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Q22:

A card is picked at random from a standard deck of cards. Let be the event that a king is picked and let be the event that a red card is picked.

Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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