Question

An ant is moving on a numbered, horizontal line every second. The number ranges from −[infinity] to [infinity] . It moves to the left integer with a probability of 1/4 and to the right integer with a probability of 3/4. Suppose initially it starts at 0, so what is the probability that after 3 seconds it will be at 1?

Answer 1

Answer:

9/32

Step-by-step explanation:

given that an ant is moving on a numbered, horizontal line every second

Probability for moving left = 1/4

and prob for moving right =3/4

As this totals 1, there is no chance that ant will remain in the same posiiton after 1 second.

Either it has to move left or right.

Initial position is 0.

After 3 seconds it is in position 1.

The chances are I second move left, next second, move right and come to 0 and third second move to 1.  

Or

I second move right, then left to 0, and third again to right to 1.

There are no other alternatives

Probability for this = $\frac{1}{4} \frac{3}{4} \frac{3}{4} +\frac{3}{4} \frac{1}{4} \frac{3}{4} \\=\frac{9}{32}$