A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day. Carry out a simulation of 20 trials using the random number table below to find the probability that the osprey will actually catch a fish on all of the next three days. Explain your method.
945 025 354 793 236
106 746 981 105 012
832 180 250 871 835
793 726 864 496 947
A) Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of the next three days is 70%.
B) Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of the next three days is 65%.
C) Using the digits 0–6 to represent a caught fish, the probability of catching a fish on each of the next three days is 35%.
D) Using the digits 0–7 to represent a caught fish, the probability of catching a fish on each of the next three days is 7%.
I know it says to show my work, but I have no clue on how to do this. (Any hints would be awesome.)
70% is .7.
Getting a fish on the next three days would be .7^3 which is .343.
Then count the numbers that have only 7 and below. There is 7 out of a total of 20. So 7/20 equals .35.
The answer is C.
Good luck!
To determine the probability that the osprey will catch a fish on all of the next three days by simulating 20 trials using the given random number table, you can follow these steps:
1. Determine the assigned values for a successful catch and a failed catch based on the provided digits.
- Option A: Using the digits 0-7 to represent a caught fish, assign a successful catch to digits 0-4 and a failed catch to digits 5-7.
- Option B: Using the digits 0-7 to represent a caught fish, assign a successful catch to digits 0-3 and a failed catch to digits 4-7.
- Option C: Using the digits 0-6 to represent a caught fish, assign a successful catch to digits 0-2 and a failed catch to digits 3-6.
- Option D: Using the digits 0-7 to represent a caught fish, assign a successful catch to digits 0 and a failed catch to digits 1-7.
2. Randomly select digits from the given random number table for each trial, with each digit representing whether the osprey caught a fish or not based on the assigned values from step 1.
3. Repeat this process for 20 trials, noting down the outcomes (successful or failed catch) for each day.
4. Calculate the percentage of trials where the osprey caught a fish on all three days and compare it to the provided options to find the correct answer.
Here's an example of running the simulation for option A (using digits 0-4 as a successful catch):
Trial 1: 945
Day 1: Successful catch (digit 4)
Trial 2: 025
Day 1: Failed catch (digit 0)
Trial 3: 354
Day 1: Successful catch (digit 4)
Trial 4: 793
Day 1: Failed catch (digit 3)
Trial 5: 236
Day 1: Successful catch (digit 4)
...
Continue this process for all 20 trials, noting down the outcomes for each day.
Finally, calculate the percentage of trials where the osprey caught a fish on all three days. For example, if there were 15 trials where the osprey caught a fish on all three days out of the 20 trials simulated, the probability would be 15/20 or 75%. Compare this result to the provided options to determine the correct answer.
Remember to repeat the simulation for each option (A, B, C, D) to find the correct answer.