There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. what is the theoretical probability of randomly drawing a red marble and then a green marble?

Total marbles = 5 + 8 + 12 = 25

P(red then green) = (5/25)(12/24) = 1/10

1/10 = 0.1 = 10%

10%

All we have to do is to multiply the probability of drawing a red marble to the probability of drawing a green marble after drawing the red one.

For the probability of drawing a red marble first, it should be a fraction with the number of red marbles as the numerator, and the total number of all marbles as the denominator.

Which means,

5/(5+8+12)

=5/25

=1/5

Now, we need to find the probability of drawing a green marble after drawing a red marble. In short, it means the number of green marbles as the numerator and the total number of all marbles one red marble (since it has been drawn already) as the denominator.

12/(4+8+12)

=12/24

=1/2

Therefore,

1/5 x 1/2

=1/10

=0.1

=10%

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

37

step-by-step explanation: