Lesson Worksheet: Dependent and Independent Events Mathematics • 10th Grade

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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 , the probabilities are shown for the combinations of events and occurring. Are and 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 “getting a blue candy first” and “getting a red candy second” independent?

AYes
BNo

Q3:

If and and , are and independent?

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

Q4:

In which of the following scenarios are and independent events?

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

Q5:

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

Q6:

and are independent events, where and . What is the probability that neither event nor event occurs?

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.

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.

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?

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