1. Amy rolls 15 8-sided dice. What is the probability that at least 2 of the...

1. Amy rolls 15 8-sided dice. What is the probability that at least 2 of the rolls are 5s?

Answer: 0.5759

2. Amy shoots 10 arrows at a target. Each arrow hits the target (independently) with probability 0.3. What is the probability that at least 3 of the arrows hit the target?

Answer: 0.6172

3. Amy shoots 64000 arrows at a target. Each arrow hits the target (independently) with probability 0.3. What is the probability that more than 2 of the first 17 arrows hit the target?

Answer: 0.9226

4. Amy tosses 19 biased coins. Each coin comes up heads with probability 0.1. What is the probability that at least 3 of the coins come up heads?

Answer: 0.2946

5. Amy tosses 10 biased coins. Each coin comes up heads with probability 0.5. What is the probability that at most 1 of the coins come up heads?

Answer: 0.0107

Expert Solution

orchestra answered 1 year ago

Consider rolling two 6-sided dice. What is the probability that at least two of the rolls...

Consider rolling two 6-sided dice. What is the probability that at least two of the rolls have a sum that exceeds 6? at least 7 of the rolls have a sum that is even? exactly three rolls have a sum that equals 5?

Bobby rolls 2 fair 6-sided dice and considers it a "success" if the sum of the...

Bobby rolls 2 fair 6-sided dice and considers it a "success" if the sum of the die results is 5 or 6. He performs 4 trials. Martha tosses 2 fair coins and considers it a "success" if both coins land on "heads." She performs 3 trials. Heather rolls 1 fair 4-sided die and considers it a "success" if he rolls a "1." He performs 5 trials. What is the probability that exactly 2 success occur in all of the combined...

Consider rolling two regular, fair, 6-sided dice 10 times. What is the probability that at least...

Consider rolling two regular, fair, 6-sided dice 10 times. What is the probability that at least two of the rolls have a sum that exceeds 6. at least 7 of the rolls have a sum that is even. exactly three rolls have a sum equaling 5.

Find the probability of getting at least twenty-five 4's in 90 rolls of a 6-sided die....

Find the probability of getting at least twenty-five 4's in 90 rolls of a 6-sided die. Justify any approximation that you use.

If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2...

If you roll two six-sided dice, what is the probability of obtaining the following outcomes? a)2 or 3 b) 6 and 4 c) At least one 5 d) Two of the same number (two 1s, or two 2s, or two 3s, etc.) e) An even number on both dice f) An even number on at least one die

6 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least...

6 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least one die lands on 3 given that all 6 dice land on different numbers. (b) [2 marks] True or False: If X is the maximum of the 6 numbers from one roll, and Y is the minimum of the 6 numbers from one roll, then X and Y are independent random variables.

2 dice are rolled 8 times in a row. What is the probability that the combined...

2 dice are rolled 8 times in a row. What is the probability that the combined number of 4 will not come up more than 2 times in 8 rolls?

Rolling a dice 15 times, find the probability of 6 consecutive rolls have 6 distinct numbers....

Rolling a dice 15 times, find the probability of 6 consecutive rolls have 6 distinct numbers. (i.e. 423123456..., 45612335626..., etc.)

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the...

Alice rolls a pair of fair six-sided dice until a sum of 6 appears for the first time. Independently, Bob rolls two fair six-sided dice until he rolls a sum 7 for the first time. Find the probability that the number of times Alice rolls her dice is equal to or within one of the number of times Bob rolls his dice.

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice....

In the game of craps, a player (known as the shooter) rolls two fair six-sided dice. The shooter immediately loses if the sum of the dice is 2, 3, or 12 and immediately wins if the sum of the dice is 7 or 11 on the first roll. If the sum is anything else (4, 5, 6, 8, 9, or 10), that number becomes the point and the shooter rolls again. The shooter now wins by rolling that same point...

Question