1) We want to estimate the probability that the maximum of the three dice is 5 or greater. To do this, we will simulate rolling three dice for a single trial. 5 trials are shown below:
Trial 1: 3, 5, 4
Trial 2: 2, 6, 1
Trial 3: 4, 2, 2
Trial 4: 1, 2, 5
Trial 5: 3, 4, 6
Appropriately assign the value of 'proportion' that represents our estimate (through 5 trials) for the probability that the maximum of three dice is 5 or greater.
2) We want to estimate the probability that the sum of the three dice is greater than 10. To do this, we will simulate rolling three dice for a single trial. 5 trials are shown below:
Trial 1: 3, 5, 4
Trial 2: 2, 6, 1
Trial 3: 4, 2, 2
Trial 4: 1, 2, 5
Trial 5: 3, 4, 6
Appropriately assign the value of 'proportion' that represents our estimate (through 5 trials) for the probability that the sum of the three dice is greater than 10.
3) We want to estimate the probability that the range of four dice is greater than 3. To do this, we will simulate rolling four dice for a single trial. 5 trials are shown below:
Trial 1: 3, 5, 4, 1
Trial 2: 2, 6, 1, 3
Trial 3: 4, 2, 2, 1
Trial 4: 1, 2, 3, 4
Trial 5: 3, 4, 6, 2
Appropriately assign the value of 'proportion' that represents our estimate (through 5 trials) for the probability that the range of the range of four dice is greater than 3.
4) Suppose there is a game of chance played with rules listed below:
A person pays $10 to play the game.
A person rolls a six-sided fair die. If the result is 6, the person wins a prize of $20.
If a 6 is NOT rolled, the person flips a coin. If the result is heads, the person wins a prize of $15. If the result is tails, the person wins nothing.
Note: If a person pays $10 to play and wins a prize of $20, the profit of the game is $20-$10 = $10.
We want to figure out if playing this game is worth the risk. One metric used to determine this is to determine how much profit a person would win on average by playing this game MANY times. We will show 5 trials below.
Trial 1: dieRoll = 6
Trial 2: dieRoll = 2, coinFlip = heads
Trial 3: dieRoll = 5, coinFlip = tails
Trial 4: dieRoll = 1, coinFlip = heads
Trial 5: dieRoll = 6
What is our estimate of the average profit made from playing the game (based on the 5 trials)? Appropriately initialize the variable 'avg' to represent our estimate.
5) Assuming that Lebron has a 73.4% chance of making a free throw on any attempt, estimate the probability that Lebron would miss two or more free throws with three attempts.
random() returns a value in the interval [0,1)
Let anything less than or equal to .734 indicate a make, and greater than .734 as a miss.
Trial 1: .791, .555, .988
Trial 2: .468, .332, .712
Trial 3: .811, .025, .795
Trial 4: .356, .665, .612
Trial 5: .199, .024, .897
What is our estimate for the probability that Lebron will miss 2 or more free throws out three (based on the five trials)? Appropriately initialize the value of 'proportion' to represent our estimate.
6) To “Get out of Jail” in Monopoly a player has to roll doubles on a pair of dice, which means both dice result in the same number.
Estimate the probability that you would have to roll less than 6 times before you obtain doubles. Five trials are shown below:
Trial 1: (6, 4), (5, 4), (2, 2)
Trial 2: (3,3)
Trial 3: (1,2), (3,4), (5,2), (6,4), (2,3), (3,1), (3,3)
Trial 4: (3,5), (4, 2), (4,3), (6,6)
Trial 5: (2,3), (3,5), (1,1)
Based on our five trials, appropriately initialize the value of 'proportion' to represent our estimate.