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# Probability that a lobster will choose tunnel

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A lobster is placed in a tank in which it is given the choice of four tunnels (a, b, c, or d) to travel through. At the opposite end of each tunnel is a cage housing 1 of four types of food. The experiment is conducted 7 separate times and the lobster chooses tunnel 'a' in 5 of the 7 trials.

What is the probability that the lobster would have chosen the 'a' tunnel 5 times in 7 trials?

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Please see the attached file for proper format, and the table.

A lobster is placed in a tank in which it is given the choice of four tunnels (a, b, c, or d) to travel through. At the opposite end of each tunnel is a cage housing 1 of four types of food. The experiment is conducted 7 separate times and the lobster chooses tunnel "a" in 5 of the 7 trials.

What is the probability that the lobster would have chosen the "a" tunnel 5 times in 7 trials?

This problem is modeled by a binomial random variable X. This assumes that the 7 trials in the experiment are independent and the probability of choosing tunnel "a" is .25. The probability is assumed to be .25 in each of the 7 trials

The parameters of X are: 7 and 0.25

You can briefly describe the distribution of X as: 7 0.25

The possible outcomes X are the integers from 0 to 7. If you want to find the probability of one of these outcomes, you use the binomial probability function:

For example, if you want to know the probability that X equals 1 and the probability that X = 2 you can use the binomial probability function to get 0.3115 and 0.3115.

0.3115 (Where 7, 0.25, and 1)
0.3115 (Where 7, 0.25, and 2)

If you use the binomial probability function on all possible outcomes of X, you can make a table listing all possible outcomes along with their probabilities. The table you get if you do this is shown below. The column on the left lists all possible outcomes of X. The binomial probability function was used to find the middle column, labeled . The column on the right, labeled is the sum of the probabilities in the middle column from up to . I have highlighted in yellow the cell showing that:

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