Worksheet: Compound Events

In this worksheet, we will practice finding and interpreting the probability of compound events.

Q1:

A bag contains 22 red balls and 9 green balls. One red ball is removed from the bag and then a ball is drawn at random. Find the probability that the drawn ball is red.

  • A 3 1 0
  • B 2 1 3 1
  • C 7 1 0
  • D 9 3 1

Q2:

In a sample space 𝑆, the probabilities are shown for the combinations of events 𝐴 and 𝐵 occurring. Are 𝐴 and 𝐵 independent events?

  • Ayes
  • Bno

Q3:

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

  • A1
  • B 2 9
  • C 1 1 2
  • D 1 4
  • E0

Q4:

A bag contains 8 red balls, 7 green balls, 12 blue balls, 15 orange balls, and 7 yellow balls. If two balls are drawn consecutively, without replacement, what is the probability that the first ball is red and the second is blue?

  • A 2 0 4 9
  • B 2 4 9
  • C 1 2 5
  • D 1 4 2

Q5:

In a sample space 𝑆, the probabilities are shown for the combinations of events 𝐴 and 𝐵 occurring. Are 𝐴 and 𝐵 independent events?

  • Ayes
  • Bno

Q6:

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?

  • A 1 4
  • B 1 6
  • C 1 1 2
  • D 5 1 2
  • E 1 3

Q7:

𝐴 and 𝐵 are independent events, where 𝑃(𝐴)=13 and 𝑃(𝐵)=25. What is the probability that events 𝐴 and 𝐵 both occur?

  • A 2 1 5
  • B 2 5
  • C 1 5
  • D 9 1 0
  • E 5 6

Q8:

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.

  • A 1 2
  • B 7 1 2
  • C 5 1 2
  • D 3 4

Q9:

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?

  • A 2 3
  • B 5 6
  • C 1 3
  • D 1 2
  • E 1 6

Q10:

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

  • A 1 2
  • B 1 4
  • C 3 8
  • D 5 8

Q11:

A fair coin is flipped and a fair die is rolled. What is the probability of rolling an even number on the die?

  • A 1 3
  • B 1 4
  • C 1 2
  • D 1 6

Q12:

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.

  • A 1 1 2
  • B 1 3
  • C 1 2
  • D 1 4
  • E 1 6

Q13:

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?

  • A 3 5
  • B1
  • C0
  • D 2 2 5
  • E 1 4 2 5

Q14:

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.

  • A 7 1 1
  • B 9 1 1
  • C 2 1 1
  • D 5 1 1
  • E 4 1 1

Q15:

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?

  • A 8 1 5
  • B 1 5 2 9
  • C 9 1 4 3 5
  • D 8 2 9

Q16:

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?

  • A 1 5
  • B 1 0 4 9
  • C 5 2 8
  • D 3 1 4

Q17:

A deck contains eight cards which are numbered 5, 7, 8, 9, 9, 15, 19, and 20. What is the probability of selecting a card at random which has a prime number?

  • A 1 4
  • B 3 4
  • C 1 2
  • D 3 8

Q18:

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?

  • A 8 2 1
  • B 2 2 1
  • C 1 0 2 1
  • D 2 7
  • E 5 2 1

Q19:

A bag contains colored balls, 18 of which are red. The rest of the balls are black. Two red balls are removed from the bag, and then a ball is drawn at random. What is the probability that the ball drawn is black, given that there were 99 balls in the bag at the start?

  • A 2 1 1
  • B 7 9 9 7
  • C 1 6 9 7
  • D 1 8 9 7

Q20:

For two events 𝐴 and 𝐵, when is it true that 𝑃(𝐴)𝑃(𝐵)=𝑃(𝐴𝐵)?

  • Awhen the events are dependent
  • Bwhen the events are disjoint
  • Cwhen one of the events is a subset of the other
  • Dwhen the events are intersected
  • Ewhen the events are independent

Q21:

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?

  • A 1 9 3 2
  • B 5 3 2
  • C 3 3 2
  • D 2 7 3 2
  • E 1 1 6

Q22:

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?

  • A 5 1 9
  • B 1 4 1 9
  • C 1 1 1 9
  • D 8 1 9
  • E 1 3 1 9

Q23:

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 Tyres 140 230 200 230
  • A 3 3 4 0
  • B 4 3 8 0
  • C 2 3 8 0
  • D 7 4 0

Q24:

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.

  • A 1 0 1 1
  • B 1 1 1
  • C 2 5
  • D 3 5
  • E 2 8 5 5

Q25:

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?

  • A 1 2 0
  • B 9 2 0
  • C 3 1 0
  • D 1 1 2 0
  • E 1 4

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