Name: ____________________________________________________
Day #3 - Be sure to complete as much of the packet as possible together in class as the remaining will be left for
homework. Every packet is graded for 10 pts.
Do Now: You have eight equally-sized textbooks but only enough room for five of them on your shelf. How many ways
can you arrange five of these books on the shelf?
Independent vs. Dependent Events
Go to the following website: http://www.regentsprep.org/regents/math/algebra/apr6/lindep.htm
Read over the content and answer the questions below.
****Note: When talking about probability, we denote the probability of event A occurring as P(A).
1. What makes two events independent of each other?
2. What is the formula for finding the probability of two independent events?
3. If you have a bag containing four red marbles, three blue marbles, and five yellow marbles, what is the
probability of picking a red marble?
4. After drawing the first marble from the bag, you replace the marble by putting it back in the bag.
a. How many marbles are there in the bag now?
b. What is the probability of picking a blue marble now?
c. Were the two events independent? Why or why not?
Name: ____________________________________________________
5. What causes two events to be dependent events?
**** Note: In math, we denote the probability of event B happening given that event A occurred as 𝐏(𝐁|𝐀).
6. What is the formula for finding the probability of two dependent events?
7. If you have a bag containing four red marbles, three blue marbles, and five yellow marbles, what is the
probability of picking a yellow marble?
8. After drawing the first marble from the bag, you do not replace the marble.
a. How many marbles are there in the bag now?
b. What is the probability of picking a blue marble now?
c. Were the two events independent? Why or why not?
9. When dealing with problems like these (picking things out of a bag, box, etc.), what is the main
determinant in deciding if the events are independent or dependent?
Name: ____________________________________________________
10. Flip a fair coin three times and record your results using the table below. Perform this task a total of
eight times.
Trial #
Flip #1
Flip #2
Flip #3
1
2
3
4
5
6
7
8
Based on your experiment, determine the following experimental probabilities.
a. Probability of getting a tails only once.
b. Probability of getting a tails at least once (once, twice, or three times)
c. Probability of getting all tails.
d. Probability of getting no tails.
11. The BIG question – is this experiment (flipping a fair coin three times) an example of independent or
dependent events? Justify your answer.
Watch the following video:
https://www.khanacademy.org/math/precalculus/prob_comb/independent_events_precalc/v/compo
und-probability-of-independent-events
Does the video say that this is an example of independent events or dependent events?
Name: ____________________________________________________
Let’s take a look at the theoretical side of the coin (ha! Get it?)…
12. List all of the possible outcomes for flipping a fair coin three times in a row.
Let’s start with…
HHH
13. How many total possible outcomes are there?
14. Let’s focus on just one of these outcomes – the H H H result…
a. What is the theoretical probability of getting H H H on three flips of a fair coin?
b. What is the probability of flipping a heads on the first flip?
c. What is the probability of flipping a heads on the second flip?
d. What is the probability of flipping a heads on the third flip?
e. What is the relationship between the answer to part a and the answers to parts b, c, and d?
15. Using your theoretical probability discoveries, answer the following questions:
a. Probability of getting a tails only once.
b. Probability of getting a tails at least once (once, twice, or three times)
c. Probability of getting all tails.
d. Probability of getting no tails.
Name: ____________________________________________________
16. Determine if the following events are independent or dependent events. Then, find the probability of
the events occurring.
a. Event A: Flipping a fair coin and getting a heads
Event B: Rolling a regular 6-sided dice and getting a 2
b. Given a box with seven white poker chips, two blue poker chips, and three red poker chips…
Event A: Selecting a blue chip from the box and then replacing it
Event B: Selecting a white chip from the box
c. Event A: Picking a spade from a standard deck of 52 cards and not replacing it
Event B: Picking a heart from the remaining deck of cards
d. Event A: Rolling an odd number with a regular 6-sided dice
Event B: Rolling the same dice again and rolling a 3.
e. Given a box with seven white poker chips, two blue poker chips, and three red poker chips…
Event A: Selecting a blue chip from the box and keeping the chip
Event B: Selecting a red chip from the box
f. Event A: Flipping a fair coin and getting a heads
Event B: Flipping a fair coin again and getting a tails.
Name: ____________________________________________________
17. Given that Lebron James’s free throw percentage is 75%, in your opinion, what is the probability that
Lebron James will make 10 free throws in a row?
Watch the following video to see if you’re correct…
https://www.khanacademy.org/math/probability/independent-dependentprobability/independent_events/v/lebron-asks-about-the-chances-of-making-10-free-throws
18. Are free throws independent or dependent events? Justify your answer.
19. What did Sal do to determine the probability of Lebron making 10 free throws in a row? Show the
math that he did below…
20. Using your understanding from this, what is the probability that Lebron James will make five free
throws in a row?