Decision Probability Worksheets Grade 11

1. Hana is an investment analyst evaluating two portfolio options for a client. Option A is a fixed-income bond that guarantees a return of $4,200 with certainty. Option B is a tech stock portfolio with variable returns: there is a 0.18 probability of a high return of $12,800, a 0.42 probability of a moderate return of $5,600, and a 0.40 probability of a low return of $1,200. Based on the expected monetary value, which option should Hana recommend to her client, and what is the expected value of that option?
2. Noah is a game designer creating a new carnival game. In the game, a player pays $6 to roll a fair 20-sided die numbered 1 through 20. If the number rolled is 1, the player wins $21. If the number rolled is a multiple of 6 (6, 12, or 18), the player wins $11. If the number rolled is a prime number greater than 10 (11, 13, 17, or 19), the player wins $16. For any other outcome, the player wins nothing. Calculate the expected value of the profit for Noah per game. Based on this expected value, should Noah keep the game as is, or must he adjust the prize structure to avoid an expected loss?
3. Liam is evaluating two investment strategies. Strategy A: gain $3500 with probability 0.25, lose $900 with probability 0.75. Strategy B: gain $2100 with probability 0.45, lose $500 with probability 0.55. Which strategy has the higher expected value and by how much?

…and 2 more problems

1. Charlotte is evaluating two investment strategies. Strategy A: gain $2700 with probability 0.37, lose $1200 with probability 0.63. Strategy B: gain $1700 with probability 0.62, lose $700 with probability 0.38. Which strategy has the higher expected value and by how much?
2. Aroha is evaluating two investment options. Option A: gain $3200 with probability 0.30, lose $800 with probability 0.70. Option B: gain $2100 with probability 0.50, lose $600 with probability 0.50. Which option has the higher expected value and by how much?
3. Mere is designing a board game where players spin a spinner divided into four equal sectors colored red, blue, green, and yellow. If a player lands on red, they win $12; on blue, they win $6; on green, they lose $4; and on yellow, they lose $10. What is the expected value of one spin? Should a player expect to gain or lose money in the long run?

…and 3 more problems

1. Olivia is deciding whether to launch a new eco-friendly product line. If she launches now, there is a 0.35 probability that demand will be high, earning her $45,000 profit, and a 0.65 probability that demand will be low, resulting in a $9,000 loss. If she waits one year, market research will be completed, giving her perfect information about demand. However, waiting will cost $3,000 in lost early-mover advantage, regardless of the outcome. Should Olivia launch now or wait, and what is the expected value of the better decision?
2. Sophia is evaluating two investment strategies. Strategy A: gain $2800 with probability 0.32, lose $600 with probability 0.68. Strategy B: gain $1900 with probability 0.54, lose $400 with probability 0.46. Which strategy has the higher expected value and by how much?
3. Matiu is a farmer deciding between two irrigation systems for his orchard. System A costs $2,400 to install and has a 70% chance of increasing his annual profit by $4,800 and a 30% chance of increasing it by only $1,200 due to variable rainfall. System B costs $1,800 to install and has a 55% chance of increasing his annual profit by $3,600 and a 45% chance of increasing it by $2,400. Based on the expected net profit (profit increase minus installation cost) for one year, which irrigation system should Matiu choose, and what is the expected net profit of that system?

…and 2 more problems