Answer:
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:
For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?
Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).
Succeeding on the 7th attempt, with p = 0.3. So
In which
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt