Worksheet: Dependent and Independent Events

In this worksheet, we will practice Identifying the two independent events and also calculate the probability of dependent events.

Q1:

A bag contains 7 blue marbles and 42 red marbles. A marble is drawn from the bag, recorded, and then replaced. Another marble is then drawn. What is the probability that the first marble is blue and the second is red?

  • A 4 1 3 3 6
  • B 6 4 9
  • C 1 2 4 9
  • D 3 2 8

Q2:

In an experiment a coin is flipped and a die rolled once, then the upper face of each is observed. 𝐴 is the event that the coin lands heads side up and the die lands with a prime number showing. 𝐵 is the event that the die lands with an even number showing. Find the probability of the occurrence of event 𝐵 and not 𝐴 .

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

Q3:

A bag contains 18 white balls and 9 black balls. If 2 balls are drawn consecutively without replacement, what is the probability that the second ball is black and the first one is white?

  • A 2 9
  • B 1 3
  • C 9 2 6
  • D 3 1 3

Q4:

If the two spinners shown are spun, what is the probability of the arrow landing on 9 in Spinner 1 and on 𝐵 in Spinner 2?

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

Q5:

Denote by 𝐴 and 𝐵 two independent events. Given that 𝑃 ( 𝐴 ) = 0 . 1 2 and 𝑃 ( 𝐵 ) = 0 . 7 5 , find 𝑃 ( 𝐵 𝐴 ) .

Q6:

Denote by 𝐴 and 𝐵 two independent events. Given that 𝑃 ( 𝐴 ) = 0 . 5 and 𝑃 ( 𝐵 ) = 0 . 4 8 , find 𝑃 ( 𝐴 𝐵 ) .

Q7:

𝐴 and 𝐵 are independent events, where 𝑃 ( 𝐴 ) = 5 6 and 𝑃 ( 𝐵 ) = 3 4 . What is the probability that neither event 𝐴 nor event 𝐵 occurs?

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

Q8:

A bag contains 30 red marbles, 12 green marbles, and 18 blue marbles. If two marbles are drawn one by one, replacing each marble after the color is recorded, what is the probability that the first marble is blue and the second is green?

  • A 6 5 9
  • B 9 5 9
  • C 7 1 0
  • D 1 1 0

Q9:

Denote by 𝐴 and 𝐵 two independent events. Given that 𝑃 ( 𝐵 ) = 0 . 2 8 and 𝑃 ( 𝐴 𝐵 ) = 0 . 4 6 , determine 𝑃 ( 𝐴 ) .

Q10:

A bag contains 21 red marbles, 26 green marbles, and 18 blue marbles. In an experiment, a marble is chosen at random from the bag, replaced, and then another marble is chosen. Find the probability that the two marbles are both green.

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

Q11:

Suppose 𝐴 and 𝐵 are two events such that 𝑃 ( 𝐴 ) = 5 7 and 𝑃 ( 𝐵 ) = 4 7 . Given that 𝑃 ( 𝐴 𝐵 ) = 2 7 , find 𝑃 ( 𝐴 𝐵 ) .

  • A 4 7
  • B 3 7
  • C 6 7
  • D 2 7
  • E 1 7

Q12:

A professor ran a series of lectures on the uses of plastic in manufacturing. All 30 of his students attended all of these classes. He then ran a two-hour revision class, which only 20 students attended, to help the students prepare for an upcoming test on the subject. Of the 15 students who passed the test, only 5 had not attended the revision class. Was passing the test independent of attending the revision class?

  • Ano
  • Byes

Q13:

Sophia has a bag containing 5 red, 3 purple, 9 yellow, and 13 pink marbles. She took one marble from her bag at random, kept it in her hand, and then took a second marble at random. Determine the probability that the first marble was pink and the second marble was purple. Is the event that the second marble she takes is purple independent of the event that the first marble she takes is pink?

  • A 1 3 1 8 0 , independent event
  • B 1 3 3 0 0 , dependent event
  • C 9 2 9 0 , independent event
  • D 1 3 2 9 0 , dependent event
  • E 1 3 2 9 0 , independent event

Q14:

A bag contains 15 blue balls and 10 red balls. A ball is chosen at random and the color is recorded. The ball is then replaced and another ball is chosen at random from the bag. What is the probability that the first ball is blue and the second is red?

  • A 6 2 5
  • B 9 4 0
  • C 1 2 2 5
  • D 7 3 0

Q15:

Denote by 𝐴 and 𝐵 two events in a sample space. Given that 𝑃 ( 𝐴 ) = 0 . 4 5 , 𝑃 ( 𝐵 ) = 0 . 6 , and 𝑃 ( 𝐴 𝐵 ) = 0 . 7 8 , are the events 𝐴 and 𝐵 independent?

  • Ano
  • Byes

Q16:

𝐴 and 𝐵 are independent events, where 𝑃 ( 𝐴 ) = 1 2 and 𝑃 ( 𝐵 ) = 3 7 . What is the probability that events 𝐴 occurs but event 𝐵 does not?

  • A 5 7
  • B 6 7
  • C 3 7
  • D 2 7
  • E 3 1 4

Q17:

An experiment consists of flipping a coin and rolling a six sided die once, then observing the upper faces of both. Event 𝐴 is when the coin lands tail side up and the die lands with an even number facing up. Event 𝐵 is when the coin lands head side up and the die lands with an odd number facing up. Determine the range of event 𝐶 , which is the occurrence of events 𝐴 and 𝐵 .

  • A 𝐶 =
  • B 𝐶 = { ( , 1 ) , ( , 2 ) , ( , 3 ) , ( , 4 ) , ( , 5 ) , ( , 6 ) , ( , 1 ) , ( , 2 ) , ( , 3 ) , ( , 4 ) , ( , 5 ) , ( , 6 ) } H H H H H H T T T T T T
  • C 𝐶 = { ( , 1 ) , ( , 3 ) , ( , 5 ) , ( , 2 ) , ( , 4 ) , ( , 6 ) } H H H T T T
  • D 𝐶 = { ( , 2 ) , ( , 3 ) , ( , 5 ) , ( , 6 ) , ( , 2 ) , ( , 3 ) , ( , 5 ) , ( , 6 ) } H H H H T T T T
  • E 𝐶 = { ( , 2 ) , ( , 4 ) , ( , 6 ) , ( , 1 ) , ( , 3 ) , ( , 5 ) } H H H T T T

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