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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.)

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Bob

  1. well, not using the table
    .7^3 = .343 so you can be pretty sure that C is correct
    now
    let the digits of each of those three digit numbers be our test for example. If all three are seven or below, we got a win. There are twenty of those numbers. How many of them have all digits 7 or below?
    025
    354
    236
    106 etc
    a total of 7 out of the 20 so .35
    whew :)

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    Damon

  2. Your answer there is actually incorrect Damon. If you look at the answers provided, it says "Using the digits 0–6 to represent a caught fish". So assuming that it's 6 or below, only 7 of the numbers listed are 6 or below. However, the reason yours is wrong is because if we assume 0-7 represents a caught fish.... there are 9 sets of numbers in which all 3 numbers are actually 7 or below which would put it at 45%. So for example...

    Random numbers given: Caught fish?(0-7) Caught Fish?(0-6)
    945 No No
    025 Yes Yes
    354 Yes Yes
    793 No No
    236 Yes Yes
    106 Yes Yes
    746 Yes No
    981 No No
    105 Yes Yes
    012 Yes Yes
    832 No No
    180 No No
    250 Yes Yes
    871 No No
    835 No No
    793 No No
    726 Yes No
    864 No No
    496 No No
    947 No No

    So with that being said, in the column where we assume 0-7 represents a caught fish, it's actually a 45% chance based on these numbers. If we assume that it's 0-6, like proven in the second column, it would be 35%. So yes, the answer would be C... just thought I'd clarify that.

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    Albert G.

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