Suppose we have an urn containing 9 marbles. Two are red, three are green, and four are blue. We randomly select 5 marbles from the urn, with replacement. What is the probability of selecting 3 green marbles, 1 red marble, and 1 blue marbles?

probability of selecting 3 green marbles, 1 red marble, and 1 blue marbles

Step-by-step explanation:

Given data urn containing '9' marbles

given  red marbles = 2

         green marbles =3

          blue marbles = 4

Five marbles can be selected at a time from '9' marbles in   ways

by using  formula

After simplification , we get

         total number of ways n(S) = 126

The probability of selecting '3' green marbles ,one red marble and one blue marble with replacement.

let ' E' be the event of selecting '3' green marbles ,one red marble and one blue marble with replacement.

n(E) =  ways

The required probability

on simplification , we get

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.