Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces.

a. What is the probability that both cards dealt are aces or 10-point cards (to 4 decimals)?

b. What is the probability that both of the cards are aces (to 4 decimals)?

c. What is the probability that both of the cards have a point value of 10 (to 4 decimals)?

d. A blackjack is a 10-point card and an ace for a value of 21. Use your answers to parts (a), (b), and (c) to determine the probability that a player is dealt blackjack (to 4 decimals). (Hint: Part (d) is not a hypergeometric problem. Develop your own logical relationship as to how the hypergeometric probabilities from parts (a), (b), and (c) can be combined to answer this question.)

a, 0.1433

b. 0.0045

c. 0.0905

d. 0.0483

Step-by-step explanation:

We have that the formula for hypergeometric probability is:

          (r) (N - r)

          (x) (n - x)

f (x) =

               (N)

               (n)

where r is "the number of individuals that y x value that the variable takes.

We have that the population size is 52. N = 52

The number of draws is equal to 2. n = 2

Now, knowing this we solve each one:

a. In this case the values are as follows: r = 20; x = 2

          (20) (52-20)

          (2) (2 - 2)

f (x) = = 95/663 = 0.1433

               (52)

               ( 2 )

b. In this case the values are as follows: r = 4; x = 2

          (4) (52-4)

          (2) (2 - 2)

f (x) = = 1/221 = 0.0045

               (52)

               ( 2 )

c. In this case the values are as follows: r = 16; x = 2

          (16) (52-16)

          (2) (2 - 2)

f (x) = = 20/221 = 0.0905

               (52)

               ( 2 )

d. The probability of blackjack would come being in relation to a, b, c

That is to say:

p (blackjack) = a - b - c

Replacing:

p (blackjack) = 0.1433 - 0.0045 - 0.0905 = 0.0483

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

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