Lesson Worksheet: Compound Events Mathematics • 7th Grade

In this worksheet, we will practice determining the sample space and the probability of compound events.

Q1:

If two dice are rolled, what is the probability that the sum is 4 or doubles are rolled?

  • A1
  • B29
  • C112
  • D14
  • E0

Q2:

A fair six-sided die with the numbers 1 to 6 is rolled, and a fair coin is flipped. What is the probability that the number obtained on the die is a factor of 12 and the coin lands with its heads side down?

  • A14
  • B16
  • C112
  • D512
  • E13

Q3:

In an experiment a coin is flipped and a die is rolled once. Event 𝐴 is the appearance of a head and a prime number. Event 𝐡 is the appearance of an even number. Find the probability of event 𝐴 or event 𝐡 occurring but not both.

  • A12
  • B712
  • C512
  • D34

Q4:

One letter is randomly selected from the word EVEN, and another is randomly selected from the word LETTER. What is the probability that both letters are vowels?

  • A23
  • B56
  • C13
  • D12
  • E16

Q5:

A coin is flipped three consecutive times. What is the probability of only getting one head?

  • A12
  • B14
  • C38
  • D58

Q6:

A card is drawn at random from a deck of cards numbered from 1 to 25. What is the probability that the card drawn has a number which is a factor of 10 or is even?

  • A35
  • B1
  • C0
  • D225
  • E1425

Q7:

A bag contains 16 white balls and 14 red balls. Two balls are drawn consecutively without replacement. What is the probability that both balls are white?

  • A815
  • B1529
  • C91435
  • D829

Q8:

A bag contains 6 blue balls and 15 red balls. If two balls are drawn without replacement, what is the probability of getting one blue ball and one red ball?

  • A15
  • B1049
  • C528
  • D314

Q9:

If these two spinners are spun, what is the probability that the sum of the numbers the arrows land on is a multiple of 5?

  • A821
  • B221
  • C1021
  • D27
  • E521

Q10:

A bag contains 32 balls. There are 27 red balls numbered from 1 to 27 and 5 white balls numbered from 28 to 32. If a ball is chosen at random from the bag, what is the probability that the ball is white or has an odd number?

  • A1932
  • B532
  • C332
  • D2732
  • E116

Q11:

In a sample of 55 people, 28 of them have brown hair and 22 of them have blue eyes. 5 of them have neither brown hair nor blue eyes. What is the probability that a random person from the sample has at least one of these features.

  • A25
  • B35
  • C2855
  • D111
  • E1011

Q12:

A classroom has 24 boys and 10 girls, where 10 boys and 6 girls wear glasses. Calculate the probability that a randomly selected student is a girl or wears glasses.

  • A317
  • B817
  • C517
  • D1517
  • E1017

Q13:

Three distinct coins are flipped once. Observing the upper faces, find the probability of 𝐴, where 𝐴 is the appearance of at least two consecutive tails.

  • A38
  • B34
  • C14
  • D12

Q14:

If the given spinner was spun once and a number cube was rolled once, determine the probability of rolling a four and spinning a number less than 23. Express your answer as a fraction in its simplest form.

  • A114
  • B16
  • C47
  • D221
  • E542

Q15:

If a number cube is rolled and the shown spinner is spun at the same time, find the probability of the pointer landing on 𝐴 and rolling a number greater than 5.

  • A136
  • B548
  • C516
  • D148
  • E124

Q16:

If this spinner was spun at the same time that a fair six-sided die was rolled, what is the probability of rolling an even number and spinning a number less than 24? Give your answer as a fraction in its simplest form.

  • A16
  • B316
  • C14
  • D516
  • E18

Q17:

A fair die is rolled once, and the given spinner is spun. What is the probability of rolling a prime number and the pointer landing on a blue section?

  • A732
  • B716
  • C14
  • D12

Q18:

If the shown spinner is spun, and a number cube is tossed at the same time, find the probability of rolling a number less than 4 and of the pointer landing on a π‘Œ.

  • A114
  • B112
  • C340
  • D116
  • E221

Q19:

A young boy opens a packet of breakfast cereal which says, β€œone in three packets contains a prize.” Later that day, he buys a bar of chocolate which says, β€œtwo out of every five bars contain a prize.” What is the probability that the boy does NOT win either one of those prizes that day?

  • A215
  • B15
  • C1315
  • D25
  • E35

Q20:

The shown spinner is spun once and a die is rolled. Find the probability of getting a five on the die and the spinner landing on the number 43. Express your answer as a fraction in its simplest form.

  • A0
  • B121
  • C17
  • D142
  • E16

Q21:

A die is rolled two consecutive times. What is the probability of getting an even number on the first roll and a prime number on the second?

  • A19
  • B13
  • C16
  • D14

Q22:

Suppose each of these spinners is spun once. Using a tree diagram or otherwise, find the probability that at least one of them will land on a𝑃 or an𝑆.

  • A215
  • B13
  • C15
  • D14
  • E25

Q23:

You and your friend each have a different spinner with red, blue, and green sectors. You are playing a game where you each spin your spinner and you win if at least one of them lands on green. Given that the probability the first spinner lands on green is 0.25, and the probability that the second spinner lands on green is 0.4, find the probability that only one of the spinners lands on green.

Q24:

Suppose these two spinners are spun. Determine the probability that the sum of the numbers you get is 6.

  • A120
  • B140
  • C340
  • D0

Q25:

Suppose that you spin these two spinners. What is the probability that the sum of the numbers you get is a prime number?

  • A12
  • B1124
  • C1748
  • D14
  • E13

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