Sample Spaces & Tree Diagrams
A fair 6-sided die is rolled and a 2-sided coin is flipped. What is the total number of outcomes in the sample space?
What is 12?
A restaurant menu offers 6 appetizers, 8 main courses, and 4 desserts. Assuming a meal consists of one of each, what is the total number of different 3-course meals available?
What is 192 meals?
A book club has 10 recommended books. If a member selects 3 books to read (where order does not matter), what is the total number of different selections possible?
What is 120 selections?
When drawing a single card from a standard 52-card deck, these are the odds in favor of drawing a King.
What is 1:12?
If you put 4:48 you need to simplify.
State the formula used to calculate expected value E(X) for a discrete probability distribution with outcomes x and probabilities P(x).
What is
x_1 \times P(x_1) + x_2 \times P(x_2) + ... + x_n \times P(x_n)?
If a tree diagram is drawn showing all possible outcomes of flipping four fair coins, what is the total number of final branches/outcomes?
What is 16?
Evaluate the expression
\frac{14!}{12!}
.
What is 182?
State whether selecting a 4-person committee from a group of 9 people requires Permutations or Combinations, and give the total number of possible committees.
What is Combinations and 126 committees?
A single card is drawn from a standard 52-card deck. Find the probability of drawing a Queen or a Diamond.
What is 4/13?
A raffle sells 1,000 tickets at $2 each. There is 1 grand prize of $500. What is the expected net profit/loss for someone purchasing one ticket?
What is a loss of $1.50 or (-$1.50)?
Write out the complete sample space $S$ for spinning a spinner with 3 equal sections (Red, Green, Blue) and flipping a fair coin (Heads, Tails).
What is {RH,RT,GH,GT,BH,BT}?
Find the number of distinguishable arrangements of the letters in the word MISSISSIPPI.
What is 34,650 arrangements?
A company department has 8 managers and 25 staff members. This is the total number of 5-person subcommittees that can be formed consisting of exactly 2 managers and 3 staff members.
What is 64,400 subcommittees?
A fair coin is flipped and a 6-sided die is rolled. Find the probability of flipping Heads and rolling a number greater than 4.
What is 1/6?
Based on the voter survey table below:
Voter Type: Urban Favor: 120 Oppose: 80 Urban Total: 200
Voter Type: Suburban Favor: 90 Oppose: 110 Suburban Total: 200
Total: Favor: 200 Oppose: 200 Voters: 400
If one voter is selected at random, find the probability that the voter favors the proposal, given that they are Suburban.
What is 9/20?
Two fair 6-sided dice are rolled. What is the number of distinct outcomes where the sum of the dice is strictly less than 5?
What is 6 outcomes?
At a regional track meet, 15 sprinters compete in the 100-meter dash. If gold, silver, and bronze medals are awarded for 1st, 2nd, and 3rd place, what is the number of possible medal outcomes?
What is 2,730 outcomes?
A teacher selects a group of 4 students from a class of 10 boys and 12 girls. What is the number of groups that contain exactly 3 girls and 1 boy?
What is 2,200 groups?
Two cards are drawn at random without replacement from a standard 52-card deck. Find the probability that neither card is a Spade.
What is 19/34?
Using the voter table below, find the probability that a randomly chosen voter is Urban OR Opposes the proposal.
Voter Type: Urban Favor: 120 Oppose: 80 Urban Total: 200
Voter Type: Suburban Favor: 90 Oppose: 110 Suburban Total: 200
Total: Favor: 200 Oppose: 200 Voters: 400
What is 31/40?
You draw a marble from a bag containing 1 Red and 1 Blue marble, record the color, put it back, and repeat for 3 total draws. What is the number of outcome paths on the tree diagram that result in getting at least two Red marbles?
What is 4 paths?
Find the number of distinguishable 5-digit numbers that can be formed using all five digits from the set {2, 2, 5, 5, 5}.
What is 10?
A choir director chooses 3 soloists from 7 sopranos and 2 soloists from 5 altos. What is the total number of soloist combinations possible?
What is 350 combinations?
A single card is drawn from a standard 52-card deck. Find the probability that the card is neither an Ace nor a Red card.
What is 6/13?
An investor evaluates two real estate projects:
Project X: Profit of $80,000 (P = 0.6), Profit of $20,000 (P = 0.3), Loss of $50,000 (P = 0.1).
Project Y: Profit of $150,000 (P = 0.3), Profit of $40,000 (P = 0.5), Loss of $30,000 (P = 0.2).
Calculate the expected profit for both projects and state which project the investor should choose.
What is $49,000, $59,000, and the investor should choose Project Y?