Lesson Worksheet: Dependent and Independent Events Mathematics

In this worksheet, we will practice calculating probabilities for dependent and independent events and checking if two events are independent.

Q1:

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

  • AYes
  • BNo

Q2:

A bag contains 5 red candies and 4 blue candies. I take one at random, note its color, and eat it. I then do the same for another candy. The figure below shows the probability tree associated with this problem. Are the events of β€œgetting a blue candy first” and β€œgetting a red candy second” independent?

  • ANo
  • BYes

Q3:

If 𝑃(𝐴)=0.3 and 𝑃(𝐡)=0.25 and 𝐴∩𝐡=βˆ…, are 𝐴 and 𝐡 independent?

  • AYes, they are independent.
  • BNo, they are dependent.

Q4:

In which of the following scenarios are 𝐴 and 𝐡 independent events?

  • AA die is rolled and a coin is flipped. Event 𝐴 is rolling a 6 on the die, and event 𝐡 is the coin landing with its heads side up.
  • BA student leaves their house on their way to school. Event 𝐴 is them arriving at the bus stop in time to catch the bus and event 𝐡 is them getting to school on time.
  • CA child takes two candies at random from a bag which contains chewy candies and crunchy candies. Event 𝐴 is them taking a chewy candy first and event 𝐡 is them taking a crunchy candy second.
  • DA teacher selects two students at random from a group containing five boys and five girls. Event 𝐴 is the teacher selecting a boy first, and event 𝐡 is the teacher selecting a girl second.
  • EA die is rolled. Event 𝐴 is rolling an even number and event 𝐡 is rolling a prime number.

Q5:

What is the probability of getting tails at least once if a coin is flipped three times?

  • A38
  • B12
  • C78
  • D18

Q6:

𝐴 and 𝐡 are independent events, where 𝑃(𝐴)=56 and 𝑃(𝐡)=34. What is the probability that neither event 𝐴 nor event 𝐡 occurs?

  • A58
  • B524
  • C124
  • D18
  • E2324

Q7:

Three friends were all born in the same year, which was not a leap year. Assuming that each friend’s birthday is independent of the others’ birthdays, and that every day of the year is equally likely to be a birthday, find the probability that the friends all have the same birthday.

  • A3365
  • B13
  • C148,627,125
  • D1365
  • E1133,225

Q8:

Benjamin and Sophia applied for life insurance. The company has estimated that the probability that Benjamin will live to be at least 85 years old is 0.6 and the probability that Sophia will live to be at least 85 years old is 0.25. Given that these are independent events, what is the probability they will both live to be at least 85?

Q9:

A jar of marbles contains 4 blue marbles, 5 red marbles, 1 green marble, and 2 black marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. Find the probability that the first is blue and the second is red.

  • A23
  • B0
  • C13
  • D34
  • E536

Q10:

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?

  • A29
  • B313
  • C13
  • D926

This lesson includes 40 additional questions and 209 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.