A game is played, where a die is tossed and a marble selected from a bag. Bag M contains 3 red marbles (R) and 2 green marbles (G). Bag N contains 2 red marbles and 8 green marbles. A fair six-sided die is tossed. If a 3 or 5 appears on the die, bag M is selected (M). If any other number appears, bag N is selected (N). A single marble is then drawn at random from the selected bag. Question > Find the probability that a green marble is drawn from either bag.

2/3

Step-by-step explanation:

A die has 6 sides.  If a 3 or 5 is rolled, then bag M is selected.  So the probability that bag M is selected is 2/6 = 1/3.

Likewise, if a number other than 3 or 5 is rolled, then bag N is selected.  So the probability that bag N is selected is 4/6 = 2/3.

If bag M is selected, the probability the marble is green is 2/5.  The probability that M is selected, AND the marble is green, is therefore:

(1/3) (2/5) = 2/15

If bag N is selected, the probability that the marble is green is 8/10 = 4/5.  The probability that N is selected, AND the marble is green, is therefore:

(2/3) (4/5) = 8/15

The total probability that a green marble is selected is therefore:

P = 2/15 + 8/15

P = 10/15

P = 2/3

Bag M: 3 red and 2 green = 5 total, so green = 2/5

Bag N: 2 red and 8 green = 10 total, so green = 8/10 = 4/5

Dice roll: chance of getting Bag M is 2/6  ( 2 numbers out of 6 total numbers on a die), reduces to 1/3

Chance of getting Bag N is 4/6 = 2/3

The probability of picking green = Probability of Bag M x Probability of green in bag M + probability of bag N x probability of green in bag N:

2/5 * 1/3 + 4/5 * 2/3 = 2/15 + 8/15 = 10/15 = 2/3

The probability = 2/3

a. 19,958,400

step-by-step explanation:

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584