1. An ant starts from the origin of a 2-D grid, at the point (0,0). Then each time it moves either i) right by one unit distance, e. g., from (0,0) to (1,0), ii) up by one unit distance, e. g., from (0,0) to (0,1), or iii) stay still, with probabilities 0.3, 0.2, and 0.5, respectively. After 10 moves, what is the probability that the ant ends up at point (2,5)

0.0091 = 0.91% probability that the ant ends up at point (2,5)

Step-by-step explanation:

What is needed to move from the point (0,0) to the point (2,5) after 10 moves:

5 moves of up by 1 unit.

2 moves of right by 1 unit.

10 - (5 + 2) = 3 standing still.

Probability:

2 moves of right by 1 unit, each with 0.3 probability.

5 moves of up by 1 unit, each with 0.2 probability.

3 standing still, each with 0.5 probability.

Number of ways this can happen:

Arrangments of 10 moves, with 2, 5 and 3 repetitions. So

Probability:

0.0091 = 0.91% probability that the ant ends up at point (2,5)

the last choice

step-by-step explanation:

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.