3.22 ([1] 3.70) an oil prospector will drill a succession of holes in a given area to find productive well. the probability that he is successful on a given trial is 0.2. a) what is the probability that the third hole drilled is the first to yield a productive well? b) if the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well? c) the prospector drills holes until he finds a productive well. how many holes would the prospector expect to drill?

a) 0.128

b) 0.107

c) 5

Step-by-step explanation:

P(successful on a given trial) = 0.2

P(unsuccessful on a given trial)=0.8

a) What is the probability that the third hole drilled is the first to yield a productive well?

This is possible when being unsuccessful in the first and second trial, successful in the third trial. This probability equals

=P(unsuccessful on a given trial) × P(unsuccessful on a given trial) × P(successful on a given trial) = 0.8 × 0.8 × 0.2 = 0.128

b) If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

This probability equals ≈ 0.107

c) The prospector drills holes until he finds a productive well. How many holes would the prospector expect to drill?

This probability equals

= = 5

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.