Agame has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards. find the probability of choosing two red cards and a blue card + yellow card

The probability of choosing two red cards would be 3/8, and the probability of choosing a blue card and a yellow card would be 1/30.

There are 10+4+2 = 16 cards total.

The probability of choosing 1 red card is 10/16; the probability of choosing a second red card would then be 9/15.

P(2 red) = 10/16(9/15) = 90/240 = 3/8.

The probability of choosing one blue card is 4/16; the probability of choosing a yellow card would then be 2/15.

P(blue and yellow) = 4/16(2/15) = 8/240 = 1/30.

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a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt