# Worksheet: Independent Events

In this worksheet, we will practice calculating probabilities for independent events.

**Q1: **

If and and , are and independent?

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

**Q2: **

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

- A
- B
- C
- D

**Q4: **

Three friends were all born in the same year, which was not a leap year. Assuming that each friendβs birthday is independent of the othersβ 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.

- A
- B
- C
- D
- E

**Q5: **

David and Olivia applied for life insurance. The company has estimated that the probability that David will live to be at least 85 years old is 0.6 and the probability that Olivia 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?

**Q6: **

In the given sample space , the probabilities are shown for combinations of events and occurring. Are and independent events?

- Ayes
- Bno

**Q7: **

What is the probability of tossing 3 coins and getting tails on all three?

- A
- B
- C
- D
- E

**Q8: **

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 coin is flipped. Event is rolling an even number and event is rolling a prime number.

**Q9: **

In which of the following scenarios are and independent events?

- AA bag contains strawberry and chocolate candies, where event is randomly picking a first candy from the bag, eating it, and it being chocolate and event is randomly picking a second candy from the bag, eating it, and it being chocolate.
- BA class of students contains eighteen boys and seventeen girls, and a teacher chooses two students at random, where event is the first randomly chosen student being a boy and event is the second randomly chosen student being a girl.
- CEvent is a cat landing on its feet when blown from a branch of a tree by a gust of wind, while event is a piece of toast landing with its buttered side up on the floor when accidentally knocked from a breakfast plate on the table.
- DOn a cold winterβs day, a student walks to school, where event is the student remembering to take his winter jacket and event is him arriving at school without getting too cold.
- EA fair six-sided die is rolled, where event is getting an odd number and event is getting a prime number.

**Q10: **

In the given sample space , the probabilities are shown for combinations of events and occurring. Are and independent events?

- Ano
- Byes

**Q11: **

Which of the following are two independent events?

- ADrawing a king from a deck of 52 cards without replacement and then drawing an ace.
- BDrawing a king from a deck of 52 cards and an ace from another well-shuffled deck of 52 cards.
- CDrawing an ace twice from a well-shuffled deck of 52 cards.
- DAll of the above.

**Q12: **

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.

- A
- B0
- C
- D
- E

**Q13: **

Suppose and are two events in a random experiment. Given that , , and , what are the possible values for and ?

- A, or ,
- B, or ,
- C, or ,
- D, or ,
- E, or ,