Worksheet: Compound Events

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 𝐵 is the appearance of an even number. Find the probability of event 𝐴 or event 𝐵 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:

An experiment consists of flipping a coin and rolling a fair six sided die once. Determine the probability of event 𝐴, the coin landing head side up and the dice landing with a prime number uppermost.

  • A112
  • B13
  • C12
  • D14
  • E16

Q7:

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

Q8:

A bag contains 4 white marbles, 2 black marbles, and 5 red marbles. If a marble is selected at random, find the probability of selecting a black or a red marble.

  • A711
  • B911
  • C211
  • D511
  • E411

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

A bag contains 19 balls, 5 of which are white, 6 are red, and 8 are black. If a ball is drawn at random, what is the probability of the ball being black or white?

  • A519
  • B1419
  • C1119
  • D819
  • E1319

Q14:

The table shows the number of tyres, from a sample of 800, which needed to be replaced after a range of distances. Using the table, calculate the probability that a tyre will need to be replaced after covering more than 50 kilometres.

Distance (km) D 50 50 < D 100 100 < D 150 D >150
Number of Damaged Tyres140230200230
  • A3340
  • B4380
  • C2380
  • D740

Q15:

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

Q16:

A bag contains 5 red balls, 9 yellow balls, and 6 black balls. What is the probability that a ball selected at random is red or black?

  • A120
  • B920
  • C310
  • D1120
  • E14

Q17:

A bag contains 9 white marbles, 2 black marbles, and 8 red marbles. If a marble is chosen at random from the bag, what is the probability that it is black or white?

  • A919
  • B1019
  • C219
  • D819
  • E1119

Q18:

James has a money box that contains 40quarters, 6dimes, 9nickels, and 16pennies. If he reaches into the box, what is the probability that the first coin he picks from the box is a dime or a nickel?

  • A0
  • B1571
  • C4671
  • D671
  • E971

Q19:

A bag contains 9 red marbles, 17 white marbles, and 7 blue marbles. What is the probability of drawing at random a blue or a red marble?

  • A811
  • B2633
  • C311
  • D1633
  • E1733

Q20:

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

Q21:

The given table shows the prizes at a lottery event. What is the probability of the first customer winning a microwave or a refrigerator?

PrizeVacuum CleanerMicrowaveRefrigeratorCar
Number121274
  • A15
  • B2435
  • C1235
  • D1635
  • E1935

Q22:

A bag contains 86 raffle tickets numbered 1 through 86. What is the probability that a randomly chosen ticket carries a number greater than 75 or less than 20?

  • A1043
  • B7586
  • C3186
  • D1186
  • E1543

Q23:

A set of 13 cards is numbered from 1 to 13. If a card is drawn at random without looking, determine the probability of getting a card with the number 4 or 13.

  • A413
  • B113
  • C1
  • D126
  • E213

Q24:

5 Russian, 6 Italian, and 29 French tourists went on a package vacation. If one of them is randomly selected to win a prize, what is the probability that a French or Italian tourist wins?

Q25:

A bag contains 17 balls. Given that 4 of the balls are white, 5 are red, and the rest are green, what is the probability of randomly drawing a red or green ball from the bag?

  • A517
  • B917
  • C1217
  • D1317
  • E817

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