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pentagon
3 months ago
12

A frog is sitting exactly in the middle of a board that is five feet long. Every ten seconds he jumps one foot to the left or on

e foot to the right, at random. You want to use simulation to estimate the probability that he jumps off the board in sixty seconds or less. (For example, if he jumps LLRLRL, he is still on the board, on the left-most square. If he jumps LLRLL, he has jumped off the board in fifty seconds.)
Required:
Describe how you would use the digits of a random number table to carry out this simulation.
Mathematics
1 answer:
PIT_PIT [12.4K]3 months ago
4 0

Answer:

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

  • It requires 7 jumps with 2 in the reverse direction (either left or right) for the frog to get off the board in 60 seconds.
  • Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
  • Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.

Step-by-step explanation:

A frog positioned right at the center of a 5ft long board is 2.5 ft away from either edge.

Every 10 seconds, the frog jumps left or right.

If the frog's jumps are LLRLRL, it will remain on the board at the leftmost square.

If it jumps as LLRLL, it will jump off the board after fifty seconds.

Given that the frog jumps every 10 seconds

   (using digits from a random number table)

  • It requires 7 jumps with 2 in reverse direction (either left or right) for the frog to get off the board in 60 seconds.
  • Alternatively, 3 jumps in the same direction will also lead to the frog being off the board.
  • Furthermore, it would take 5 jumps with one in the opposite direction within the time limit of 60 seconds to leave the board.
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