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
(1 point)
Responses
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%.
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%.
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%.
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%.
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%.
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%.
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%.
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%.
To simulate the osprey catching a fish on all of the next three days, we will use the random number table provided. We will consider the digits 0-7 as a successful catch (representing the 70% chance of catching a fish).
We will take groups of three digits from the random number table to represent each day. For each group of three digits, we will consider a successful catch if all three digits are between 0-7.
Let's go through the random number table for 20 trials:
Trial 1: 945 - no catch
Trial 2: 025 - catch
Trial 3: 354 - catch
Trial 4: 793 - catch
Trial 5: 236 - no catch
Trial 6: 106 - catch
Trial 7: 746 - catch
Trial 8: 981 - catch
Trial 9: 105 - catch
Trial 10: 012 - catch
Trial 11: 832 - catch
Trial 12: 180 - catch
Trial 13: 250 - catch
Trial 14: 871 - catch
Trial 15: 835 - catch
Trial 16: 793 - catch
Trial 17: 726 - catch
Trial 18: 864 - catch
Trial 19: 496 - catch
Trial 20: 947 - catch
Out of the 20 trials, the osprey caught a fish on all three days (100% success rate).
Therefore, the probability of the osprey catching a fish on all of the next three days is 100%.