When placed in a maze, a mouse has a 35% chance of finding the cheese at...

When placed in a maze, a mouse has a 35% chance of finding the cheese at the end of the maze. What is the probability of the mouse finding the cheese a) in three consecutive ways? b) in three of four attempts?

Solutions

Expert Solution

When placed in a maze, a mouse has a 35% chance of finding the cheese at the end of the maze.

So, the chance that the mouse finds the cheese is 0.35; and the chance that the mouse does not find the cheese, is 1-0.35, ie. 0.65.

Question (a)

We have to find the probability that the mouse finds the cheese at the end of the maze, in three consecutive ways.

Now, each of the times, the chance of finding the cheese is 0.35.

So, the required probability is 0.35*0.35*0.35, ie. 0.042875.

So, the probability that the mouse finds the cheese in three ways, is 0.042875.

Question (b)

We have to find the probability that the mouse finds the cheese in three of four attempts.

Now, the three ways in which the mouse finds the cheese, can be selected in ( 4 C 3 ) ways.

In each of the three attempts, the mouse finds the cheese with chance 0.35; and on the remaining time, does not find the cheese with chance 0.65.

So, the required probability is

So, the chance that the mouse finds the cheese 3 times out of 4, is 0.111475.

orchestra answered 1 year ago

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