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Lesson: Probability of Compound Events

Sample Question Videos

Worksheet • 25 Questions • 6 Videos

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

Q2:

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

  • A yes
  • B no

Q3:

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

  • A 2 9
  • B1
  • C 1 1 2
  • D0
  • E 1 4

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

Q5:

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

  • A no
  • B yes

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

Q7:

𝐴 and 𝐡 are independent events, where 𝑃 ( 𝐴 ) = 1 3 and 𝑃 ( 𝐡 ) = 2 5 . What is the probability that events 𝐴 and 𝐡 both occur?

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

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 𝐡 is the appearance of an even number. Find the probability of event 𝐴 or event 𝐡 occurring but not both.

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

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

Q10:

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

  • A 3 8
  • B 1 2
  • C 1 4
  • 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 2
  • B 1 6
  • C 1 3
  • D 1 4

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

Q13:

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

  • A 1 4 2 5
  • B1
  • C 2 2 5
  • D0
  • E 3 5

Q14:

A bag contains 10 white marbles, 7 black marbles, and 3 red marbles. If a marble is selected at random, find the probability of selecting a black or a red marble.

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

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

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

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 3 8
  • B 1 4
  • C 1 2
  • D 3 4

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 9?

  • A 1 7
  • B 8 4 9
  • C 2 5 4 9
  • D 5 4 9

Q19:

A bag contains coloured 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 1 8 9 7
  • B 2 1 1
  • C 7 9 9 7
  • D 1 6 9 7

Q20:

For two events 𝐴 and 𝐡 , when is it true that 𝑃 ( 𝐴 ) β‹… 𝑃 ( 𝐡 ) = 𝑃 ( 𝐴 ∩ 𝐡 ) ?

  • A when the events are independent
  • B when the events are dependent
  • C when the events are disjoint
  • D when the events are intersected
  • E when one of the events is a subset of the other

Q21:

A bag contains 32 balls. There 27 red balls, which are numbered from 1 to 27, and 5 white balls which are 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 1 1 6
  • C 2 7 3 2
  • D 3 3 2
  • E 5 3 2

Q22:

A bag contains 18 balls, 5 of which are white, 9 are red, and 4 are black. If a ball is drawn at random, what is the probability of the ball being white or red?

  • A 7 9
  • B 5 1 8
  • C 1 3 1 8
  • D 1 2

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 2 3 8 0
  • C 4 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 3 5
  • C 2 8 5 5
  • D 1 1 1
  • E 2 5

Q25:

A bag contains 5 red balls, 2 yellow balls, and 4 black balls. What is the probability that a ball selected at random is red or yellow?

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