Expected Value & Payoffs
Sequential Selection
Conditional Probability
Independence & Weather
Potpopurri
100
A carnival game costs $0 to spin a wheel with 8 equal sections: 1 section pays $16, 2 sections pay $8, and 5 sections pay $0. What is the expected payout per spin?
What is $4.00?
100
A bakery owner notices that 80% of customer orders exceed $20. Assuming orders are independent, what is the probability that the next 2 consecutive sales both exceed $20?
What is 16/25?
100
If one employee is selected at random, what is the probability that they prefer fully remote work?
What is 3/8?
100
A fair 6-sided die is rolled twice. Event A is "even on the first roll" and Event B is "odd on the second roll". Are events A and B independent?
What is yes?
100
A raffle bucket contains 15 red tickets, 25 blue tickets, and 10 golden tickets. If 1 ticket is drawn at random, what is the probability of selecting a ticket that is NOT blue?
What is 1/2?
200
A library tracks daily computer lab issues: 0 issues (p = 0.50), 1 issue (p = 0.30), 2 issues (p = 0.15), and 3 issues (p = 0.05). What is the expected number of daily equipment issues?
What is 0.75 issues?
200
An animal shelter has 10 kittens: 4 tabbies, 3 calicos, and 3 Siamese. If two adopters select kittens at random with replacement, what is the probability both select a tabby?
What is 4/25?
200
Find the probability that a randomly chosen employee is in Marketing, given that they prefer fully remote work.
What is 5/9?
200
For a fair 6-sided die rolled twice, what is the probability of rolling a number greater than 4 on the first roll AND an odd number on the second roll?
What is 1/6?
200
A high school fundraiser charges $5 per ticket for a 50-ticket raffle. There is 1 grand prize of $100 and 4 runner-up prizes of $25. What is the expected net value (profit or loss) of buying 1 ticket?
What is a loss of $1 or -$1?
300
A vendor expects $80,000 net profit at an outdoor festival, but severe heat would reduce net profit to $20,000. The probability of severe heat is 0.25. What is the vendor's expected net profit?
What is $65,000?
300
A box contains 12 markers: 5 red, 4 blue, and 3 green. If two markers are drawn at random without replacement, what is the probability both are red?
What is 5/33?
300
Find the probability that an employee prefers Hybrid work, given that they are in Engineering.
What is 1/2?
300
The unconditional probability of airport flight delays on any day is 0.30. The probability of a delay following a delayed day is 0.70. What is the probability of flight delays on two randomly selected consecutive days?
What is 0.21 or 21%?
300
A drawer contains 8 black socks and 4 white socks. If you pull out 2 socks at random without replacement, what is the probability of drawing 2 white socks (expressed as a fraction in simplest form)?
What is 1/11?
400
A sales representative is being assigned 2 new client accounts. Account A has a 40% chance of adding $50,000 in volume, and Account B has a 60% chance of adding $30,000 in volume. What is her total expected additional volume?
What is $38,000?
400
Two cards are dealt successively without replacement from a standard 52-card deck. What is the probability that the first card is a Heart and the second card is a Spade?
What is 13/204?
400
What is the probability that a randomly selected employee is in Engineering AND prefers On-Site work.
What is 1/12?
400
In a mountain valley, the probability of snow on any given day is 0.40. However, because storm fronts tend to linger, the probability of snow on a day following a snowy day increases to 0.85. What is the probability that it snows on two consecutive days, and are these two weather events dependent or independent?
What is 0.34 and dependent?
400
A game requires flipping a fair coin and spinning a 5-equal-section spinner numbered 1 through 5. What is the probability of getting Heads on the coin AND a prime number on the spinner?
What is 3/10?
500
A vendor expects $80,000 net profit at an outdoor festival, but severe heat would reduce net profit to $20,000. The probability of severe heat is 0.25. If the vendor buys an insurance policy for $15,000 that pays $80,000 in case of severe heat, what is the expected net profit?
What is $70,000?
500
Two cards are dealt successively without replacement from a standard 52-card deck. What is the conditional probability that the second card is a Diamond, given that the first card dealt was a Diamond?
What is 4/17?
500
What is the probability that an employee is in Marketing, given that they do not prefer On-Site work?
What is 4/9?
500
In a coastal town, the probability of rain on Day 1 is 2/5. If it rains on Day 1, the probability of rain on Day 2 increases to 3/4. If it does not rain on Day 1, the probability of rain on Day 2 is 1/6. What is the probability that it rains on at least one of the two consecutive days, and are rain on Day 1 and rain on Day 2 independent or dependent?
What is 1/2 and dependent?
500
A drawer contains 4 white socks, 3 grey socks, and 3 black socks. If you randomly pull out 2 socks without replacement, what is the probability of drawing a matching pair?
What is 4/15?