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An ant is moving on an integer-numbered, horizontal line every second. The number ranges from −∞...

An ant is moving on an integer-numbered, horizontal line every second. The number ranges from −∞ to −∞. 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, what is the probability that three seconds later it will be at 1?

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Answer #1

P( moving to a left integer ) = 1/4

P( moving to a right integer) = 3/4

P( Starting from 0 after 3 seconds later it will be at 1 )

= P( from 0 to -1, -1 to 0 & 0 to 1) + P( 0 to 1, 1 to 2 & 2 to 1)

= P( 0 to -1) * P( - 1to 0) * P( 0 to 1) + P( 0 to 1) * P( 1 to 2) * P( 2 to 1)

=(1/4) * (3/4) * (3/4) + (3/4) (3/4) * (1/4)

=9/32

=0.28125

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