There are 98 balls in a box. 25 of them are red, 19 of them are green, 30 of them are purple, and 24 of them are blue. Suppose Hao draws 22 balls from the box with replacement (he draws the ball, records its color, and then puts it back into the box). Find the probability that he draws 2 red balls, 5 green balls, 10 purple balls, and 5 blue balls

1.1348621526 X 10⁻¹³

Step-by-step explanation:

Number of Red balls=25

Number of Green balls=19

Number of Purple balls=30

Number of Blue=24

Total=25+19+30+24=98

Since the balls are picked with replacements, probability of picking a color will be the same all true.

P(Picking a red ball)= 25/98

P(Picking a green ball)= 19/98

P(Picking a purple ball)= 30/98

P(Picking a blue ball)= 24/98

P(2 red balls)= 25/98 X 25/98 = (25/98)²

P(5 green balls)= 19/98 X 19/98 X 19/98 X 19/98 X 19/98 =(19/98)⁵

P(10 purple balls)= 30/98 X 30/98 X 30/98 X 30/98 X 30/98 X 30/98 X 30/98 X 30/98 X 30/98 X 30/98 =(30/98)¹⁰

P( 5 blue balls) =24/98 X 24/98 X 24/98 X 24/98 X 24/98 =(24/98)⁵

P(2 red balls, 5 green balls, 10 purple balls, and 5 blue balls) = (25/98)² X (19/98)⁵ X (30/98)¹⁰ X (24/98)⁵

=1.1348621526 X 10⁻¹³

Probability = 1.0015 * 10 ^ -3

Step-by-step explanation:

Number of Red balls=25

Number of Green balls=19

Number of Purple balls=30

Number of Blue=24

Total=25+19+30+24=98

He draws 22 balls with replacement.

So arrangement doesn't matter.

Probability of 2 red balls, 5 green balls, 10 purple balls, and 5 blue balls is =

( 25C2 * 19C5 * 30C10 *24C5)/98C22

Note the C represent combination.

=( 300*11628*30045015*42504)/(4.448120577*10^21)

= 1.0015 * 10 ^ -3

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.