Suppose that k events b1, b2, bk form a partition of the sample space s. for i = 1, k, let p r(bi) denote the prior probability of bi . there is another event a that p r(a) > 0. let p r(bi |a) denote the posterior probability of bi given that the event a has occurred. prove that if p r(b1|a) < p r(b1), then p r(bi |a) > p r(bi) for at least one value of i (i = 2, k). (hint: one or more of these tricks might : p(bi |a)p(a) = p(bi ∧ a), pk i=1 p(bi) = 1, pk i=1 p(bi |a) = 1, p(bi ∧ a) + p(bi ∧ ¬a) = p(bi), pk i=1 p(bi ∧ a) = p(a))

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

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.

correct answer:

b.(19,-2)

or