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

Q2:

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 1 2 5
  • C 1 4 2
  • D 2 4 9

Q3:

A bag contains 5 red balls, 9 green balls, 18 blue balls, 7 orange balls, and 6 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 3 4 5
  • B 2 4 5
  • C 1 4 4
  • D 1 2 2

Q4:

A bag contains 9 red balls, 5 green balls, 10 blue balls, 10 orange balls, and 16 yellow balls. If two balls are drawn consecutively, without replacement, what is the probability that the first ball is blue and the second is orange?

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

Q5:

A bag contains 7 red balls, 7 green balls, 14 blue balls, 10 orange balls, and 11 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 3 7
  • B 2 4 9
  • C 1 4 8
  • D 1 2 4

Q6:

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

Q7:

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

  • A 1 4
  • B 1 1 2
  • C0
  • D 2 9
  • E1

Q8:

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

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?

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

Q10:

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

Q11:

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

Q12:

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

Distance D 50 50 D 100 100 D 150 D 150
Number of Damaged Tires 140 230 200 230
  • A
  • B
  • C
  • D

Q13:

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

Q14:

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

Q15:

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?

  • A 1 0 1 9
  • B 8 1 9
  • C 9 1 9
  • D 1 1 1 9
  • E 2 1 9

Q16:

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

Q17:

Miles has a money box that contains 40 quarters, 6 dimes, 9 nickels, and 16 pennies. 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?

  • A 6 7 1
  • B0
  • C 9 7 1
  • D 1 5 7 1
  • E 4 6 7 1

Q18:

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?

  • A 8 1 1
  • B 2 6 3 3
  • C 3 1 1
  • D 1 6 3 3
  • E 1 7 3 3

Q19:

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.

  • A 5 1 7
  • B 1 5 1 7
  • C 3 1 7
  • D 1 0 1 7
  • E 8 1 7

Q20:

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

Q21:

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 1 2
  • C 1 3
  • D 5 1 2
  • E 1 6

Q22:

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

Prize Vacuum Cleaner Microwave Refrigerator Car
Number 10 2 6 4
  • A 1 1 1
  • B 2 1 1
  • C 8 1 1
  • D 3 1 1
  • E 5 1 1

Q23:

A bag contains 54 raffle tickets numbered 1 through 54. What is the probability that a randomly chosen ticket carries a number greater than 39 or less than 10?

  • A 5 1 8
  • B 2 5 5 4
  • C 5 2 7
  • D 4 9
  • E 1 3 1 8

Q24:

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

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

Q25:

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